Matrices

CBSE Class 12 Mathematics · every board question from this chapter, 2023–2026 · 69 of them repeated across years

• If matrix A=[ ] is such that A^2=I, then:2026
• If A=[ ] and A+A^′=I, then θ is equal to:2026
• For any square matrix A with real entries, if A + A' is a symmetric matrix then:2026
• If A=[a ij] is a 2 × 2 matrix whose elements are given by a ij=( i-3 j )/2, then A' is:2026
• If A and B are square matrices of same order, then which of the following statements is/are always true? (i) (A+B)(A-B)=A^2-B^2…2026asked 3×
• Let A=[a ij] be a 2 × 2 matrix whose elements are given by a ij=((i+2 j)^2)/3. Then A^′ is given by:2026
• If A is a square matrix such that A^2=A, then (A-I)^3-A is equal to:2026
• Let A=[a ij] be a 2 × 2 matrix whose elements are given by a ij=((2 i-j)^2)/3. Then A^′ is:2026
• Which of the following cannot be the order of a row-matrix?2026
• If A is a symmetric matrix, then for any matrix B of order same as A, BAB' is a/an:2026
• A matrix B=[b ij] m × m is said to be a diagonal matrix, if:2026
• If A^2=4 A+3 I and A^-1=xA+yI, then the value of (x+y) is:2026asked 3×
• If A and B are skew-symmetric matrices of same order, then AB^′+BA^′ is a/an:2026asked 3×
• Which of the following properties is/are true for two matrices of suitable orders? (i) (A+B)^′=A^′+B^′ (ii) (A-B)^′=B^′-A^′ (iii)…2026asked 3×
• If A=[ ] is a symmetric matrix, then the value of 3 a+b+c is2026asked 3×
• If A=[ ] and A+A^′=I, then the value of x ∈[0, (π)/2] is2026
• Let A=[ ] and B=[ ]. If A+B+C=O, then matrix C is:2026asked 3×
• If [ ] A=[ ], then order of A must be:2026
• For a square matrix A, (3 A)^-1=2026asked 3×
• If a square matrix A is such that A^2=A and (I-A)^3=xA+I, then value of x must be:2026asked 3×
• If A is a non-singular matrix, then which of the following is not true?2026asked 3×
• If A and B are skew symmetric matrices of same order, then which of the following matrices is also skew symmetric?2026
• If A=[a ij] 3 × 3 is a scalar matrix then which of the following must be true?2026
• If a matrix X is such that [2 1] X = [3 4 5], then the order of matrix X is:2026
• If A=[ ] and A+A^′=2 I, then value of x ∈[0, (π)/2] is2026
• If A and B are symmetric matrics of same order, then (AB-BA) is a2026
• Which of the following cannot be an order of a column-matrix?2026
• If a matrix B is such that B[ ]=[ ], then the order of matrix B is: matrix B is:2026
• If A=[ ] and A+A^′=I, then value of x ∈[(-π)/2, (π)/2] is2026
• If A and B are symmetric matrices of same order, then which of the following matrices is a skew-symmetric matrix?2026
• Assertion: If A and B are two square matrices such that AB and BA are defined, then it is not necessary that AB=BA. Reason (R):…2026asked 3×
• If A=[ ], then compute A^2-4 A-5 I.2026
• If A=[ ], then compute A^2-5 A+4 I.2026
• If A=[ ], then compute A^2-7 A+10 I.2026
• Find cost (per kg) of each fertilizer A, B and C that the farmer needs to buy, such that 1 kg each of fertilizer A and C added to…2026
• A man goes to buy fruits from the market. The shopkeeper informs him that 4 apples, 3 oranges and 2 bananas cost ₹ 60; 2 apples,…2026
• Three students A, B and C go to a book-store to buy art books, story books and puzzle solving books. A buys one of each type of…2026
• If P=[ ] and Q=[ ], find (QP) and hence solve the following system of equations using matrices: x-y=3,2 x+3 y+4 z=17, y+2 z=7 OR…2026asked 3×
• If A=[ ], find A^-1 and use it to solve the following system of equations: -2 y+z=7,2 x-y-z=8, x-2 y=10 OR If [ ] is a singular…2026asked 3×
• On the inauguration day of a new showroom, a lucky draw was organized and some vouchers of ₹ 1,000 and ₹ 500 were given to the…2026asked 3×
• A carpenter needs to design a wooden box in the shape of a cuboid such that the sum of its length and breadth is 3 cm more than…2026asked 3×
• Let both AB^′ and B^′ A be defined for matrices A and B. If order of A is n × m, then the order of B is:2025asked 3×
• If A=[ ], then A^3 is:2025asked 3×
• If A=[ ], then A is a:2025
• If A and B are square matrices of same order such that AB=A and BA=B, then A^2+B^2 is equal to:2025asked 3×
• If A=[ ], then A is a/an:2025
• If A=[ ], then A is a:2025
• What is the total number of possible matrices of order 3 × 3 with each entry as √2 or √3?2025asked 3×
• If A and B are two square matrices of the same order, then (A+B)(A-B) is equal to:2025
• If A=kB, where A and B are two square matrices of order n and k is a scalar, then:2025
• If A=[ ] and B=[ ], then the correct statement is:2025
• Let P be a skew-symmetric matrix of order 3. If det(P)=α, then (2025)^α is2025
• The matrix A=[ ] is a/an:2025asked 3×
• If A=[ ] is a symmetric matrix, then (2 x+y) is2025
• If A and B are square matrices of same order, then (AB^T-BA^T) is a2025
• Sum of two skew-symmetric matrices of same order is always a/an:2025asked 3×
• If A is a square matrix of order 3 such that det =9, then det(9 A^-1) is equal to2025
• If [ ]=[ ], then (x-y)=?2025
• If M and N are square matrices of order 3 such that det(M)=m and MN=mI, then det(N) is equal to:2025
• If [ ]=[ ], then the value of (x-y) is:2025asked 3×
• If A and B are invertible matrices of order 3 × 3 such that det =4 and det[(AB)^-1]=1/20, then det is equal to:2025
• If a matrix A is both symmetric and skew-symmetric, then A is a:2025
• Four friends Abhay, Bina, Chhaya and Devesh were asked to simplify 4 AB+3(AB+BA)-4 BA, where A and B are both matrices of order 2…2025asked 3×
• Let A and B be two matrices of suitable orders. Then, which of the following is not correct?2025
• If [ ] is a singular matrix, then the value of x is:2025
• Which of the following can be both a symmetric and skew-symmetric matrix?2025asked 3×
• Let A=[ ], B=[ ], C=[ ], which of the following is defined?2025asked 2×
• Let A be a matrix of order m × n and B is a matrix such that A^T B and B A^T are defined. Then, the order of B is:2025
• The matrix [ ] is a:2025asked 3×
• A system of linear equations is represented as AX=B, where A is coefficient matrix, X is variable matrix and B is the constant…2025
• If A=[ ], then A^-1 is2025asked 3×
• If A=[ ] is a scalar matrix, then y^x is equal to2025
• Let A=[a ij] be a square matrix of order 3 such that a ij= j-2 i. Then which of the following is true?2025
• If A and B are invertible matrices, then which of the following is not correct?2025asked 3×
• If A and B are square matrices of order m such that A^2-B^2=(A-B)(A+B), then which of the following is always correct?2025asked 3×
• Assertion: A =diag[ ] is a scalar matrix of order 3 × 3. Reason (R): If a diagonal matrix has all non-zero elements equal, it is…2025asked 3×
• If A=[ ] and A^2=kA, then find the value of k.2025
• If [ ] A=[ ], then find matrix A.2025
• If A=[ ], then find the value of K if A^2=6 A+K I 2, where I 2 is an identity matrix.2025
• If A=[ ], then show that A^2-4 A+7 I=0.2025
• Let A=[ ] and C=[ ] be two matrices. Then, find the matrix B if AB=C.2025
• Find the value of x, if [ ][ ][ ]=O.2025
• If A=[ ], B=[ ] and C=[ ], are three matrices, then find ABC.2025
• Let 2 x+5 y-1=0 and 3 x+2 y-7=0 represent the equations of two lines on which the ants are moving on the ground. Using matrix…2025asked 3×
• If A is a 3 × 3 invertible matrix, show that for any scalar k ≠ 0, (kA)^-1=1/(k) A^-1. Hence calculate (3 A)^-1, where A=[ ]2025asked 3×
• A furniture workshop produces three types of furniture - chairs, tables and beds each day. On a particular day the total number…2025
• Three students run on a racing track such that their speeds add up to 6 km / h. However, double the speed of the third runner…2025
• An amount of ₹ 10,000 is put into three investments at the rate of 10 %, 12 % and 15 % per annum. The combined annual income of…2025
• Given A=[ ] and B=[ ], find AB. Hence, solve the system of linear equations: OR If A=[ ], then find A^-1. Hence, solve the system…2025asked 3×
• A school wants to allocate students into three clubs: Sports, Music and Drama, under following conditions: - The number of…2025asked 3×
• Three students, Neha, Rani and Sam go to a market to purchase stationery items. Neha buys 4 pens, 3 notepads and 2 erasers and…2025asked 3×
• If A=[a ij] is an identity matrix, then which of the following is true?2024asked 3×
• If [ ] is a scalar matrix, then the value of a+2 b+3 c+4 d is:2024asked 3×
• If the sum of all the elements of a 3 × 3 scalar matrix is 9, then the product of all its elements is:2024asked 3×
• If A=[ ] is a skew-symmetric matrix, then the value of 2 a-(b+c) is:2024
• If A is a square matrix of order 2 and A =-2, then value of 5 A^′ is:2024
• If a matrix has 36 elements, the number of possible orders it can have, is:2024asked 3×
• For the matrix A=[ ] to be invertible, the value of λ is:2024
• Given that A^-1=1/7[ ], matrix A is:2024asked 3×
• If A=[ ], then the value of I-A+A^2-A^3+… is:2024asked 3×
• If inverse of matrix [ ] is the matrix [ ], then value of λ is:2024asked 3×
• If A=[ ] and A^2+7 I=kA, then the value of k is:2024
• If A=[ ] and B=[ ], then value of x for which A^2=B is:2024
• If [ ][ ]=[ ][ ], then value of x is:2024
• If A=[ ] and A^2-kA-5 I=O, then the value of k is:2024
• If [ ]=[ ], then the value of (24/(x)+24/(y)) is:2024asked 3×
• Let A=[ ] and B=1/3[ ]. If AB=I, then the value of λ is:2024
• Given that [ ][ ]=0, the value of x is:2024
• The product of matrix P and Q is equal to a diagonal matrix. If the order of matrix Q is 3 × 2, then order of matrix P is:2024
• If for the matrix A=[ ], A+A^′=2 √3 I, then the value of x ∈[0, (π)/2] is:2024
• If matrices A and B are of order 1 × 3 and 3 × 1 respectively, then the order of A^′ B^′ is:2024
• The number of all scalar matrices of order 3, with each entry -1,0 or 1, is:2024
• Find the matrix A^2, where A=[a ij] is a 2 × 2 matrix whose elements are given by a ij= maximum ( i, j ) - minimum ( i, j ):2024asked 3×
• For any square matrix A,(A-A^′) is always2024
• If A and B are two skew symmetric matrices, then (AB+BA) is:2024asked 2×
• If A=[a ij] be a 3 × 3 matrix, where a ij=i-3 j, then which of the following is false?2024asked 2×
• If F(x)=[ ] and [F(x)]^2=F(k x), then the value of k is:2024asked 2×
• If A and B are two non-zero square matrices of same order such that (A+B)^2=A^2+B^2, then:2024asked 2×
• Assertion: For any symmetric matrix A, B^′ AB is a skew-symmetric matrix. Reason (R): A square matrix P is skew-symmetric if…2024asked 3×
• Assertion: Every scalar matrix is a diagonal matrix. Reason (R): In a diagonal matrix, all the diagonal elements are 0.2024asked 3×
• If A=[ ], find A^-1 and use it to solve the following system of equations: x-2 y=10,2 x-y-z=8,-2 y+z=7 OR If A=[ ] and A^-1=[ ],…2024asked 3×
• If A=[ ] and B^-1=[ ], find (AB)^-1. Also, find (AB)^-1. OR Given A=[ ], find A^-1. Use it to solve the following system of…2024
• Solve the following system of equations, using matrices: 2/(x)+3/(y)+10/(z)=4, 4/(x)-6/(y)+5/(z)=1, 6/(x)+9/(y)-20/(z)=2 where x,…2024asked 2×
• Use the product of matrices ( )( ) to solve the following system of equations:2024
• A scholarship is a sum of money provided to a student to help him or her pay for education. Some students are granted…2024asked 3×
• If A=[ ] is a symmetric matrix, then the value of x+y+z is:2023
• If A=[ ], then A^2023 is equal to2023
• If A is a 3 × 4 matrix and B is a matrix such that A^′ B and AB^′ are both defined, then the order of the matrix B is:2023
• If [ ][ ]=[ ], then the value of (2 x+y-z) is:2023
• If for a square matrix A, A^2-3 A+I=O and A^-1=xA+yI, then the value of x+y is:2023asked 3×
• If x[ ]+y[ ]=[4/9], then:2023asked 3×
• If [ ]=P+Q, where P is a symmetric and Q is a skew symmetric matrix, then Q is equal to2023asked 3×
• Let A be a skew-symmetric matrix of order 3. If A =x, then (2023)^x is equal to:2023
• If A=[ ] and A=A^T, where A^T is the transpose of the matrix A, then2023
• If A is a square matrix and A^2=A, then (I+A)^2-3 A is equal to:2023asked 2×
• If for a square matrix A, A^2-A+I=O, then A^-1 equals2023asked 2×
• A and B are skew-symmetric matrices of same order. AB is symmetric, if:2023asked 3×
• If a matrix A=[ ], then the matrix AA^′ (where A^′ is the transpose of A ) is:2023asked 3×
• For what value of x ∈[0, (π)/2], is A+A^′=√3 I, where A=[ ]?2023asked 2×
• If A=[a i j] is a square matrix of order 2 such that a ij=., then A^2 is2023
• If A=[ ] and 2 A+B is a null matrix, then B is equal to:2023asked 2×
• If A=[ ], B=[ ] and A=B^2, then x equals2023asked 2×
• The product [ ][ ] is equal to:2023asked 2×
• Number of symmetric matrices of order 3 × 3 with each entry 1 or -1 is2023
• A and B are square matrices of same order. If (A+B)^2=A^2+B^2, then:2023
• If [ ] is a singular matrix, then the product of all possible values of x is:2023
• If A=[ ] and (3 I+4 A)(3 I-4 A)=x^2 I, then the value (s) x is/are:2023asked 3×
• If A is a 2 × 3 matrix such that AB and AB^′ both are defined, then order of the matrix B is2023
• If A=[ ], then show that A^3-23 A-40 I=O.2023
• Find the inverse of the matrix A=[ ]. Using the inverse, A^-1, solve the system of linear equations x-y+2 z=1; 2 y-3 z=1; 3 x-2…2023asked 3×
• If A=[ ], B=[ ], then find AB and use it to solve the following system of equations: OR If f(α)=[ ], prove that f(α) ·…2023asked 3×
• If A=[ ] and B^-1=[ ], find (AB)^-1. OR Solve the following system of equations by matrix method:2023asked 3×
• If A=[ ], then show that A^3-6 A^2+7 A+2 I=O. OR If A=[ ], then find A^-1 and use it to solve the following system of equations:…2023asked 3×
• Gautam buys 5 pens, 3 bags and 1 instrument box and pays a sum of ₹ 160. From the same shop, Vikram buys 2 pens, 1 bag and 3…2023asked 3×

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