✓ Board-verified
Mathematics · 2025 · 2 marks
CBSE 2025 · Region 7 · Set 1 · Q22
If A = [2, 3; -1, 2], then show that A^2-4 A +7 I =0.
If $\displaystyle \mathrm{A}=\left[\begin{array}{rr}2 & 3 \\ -1 & 2\end{array}\right]$, then show that $\displaystyle \mathrm{A}^{2}-4 \mathrm{~A}+7 \mathrm{I}=0$.
Marking-scheme solution
\[\begin{aligned}
& \mathrm{A}^{2}=\left[\begin{array}{cc}
2 & 3 \\
-1 & 2
\end{array}\right]\left[\begin{array}{cc}
2 & 3 \\
-1 & 2
\end{array}\right]=\left[\begin{array}{cc}
1 & 12 \\
-4 & 1
\end{array}\right] . \\
& \text { L.H.S. }=\mathrm{A}^{2}-4 \mathrm{A}+7 \mathrm{I}=\left[\begin{array}{cc}
1 & 12 \\
-4 & 1
\end{array}\right]-\left[\begin{array}{cc}
8 & 12 \\
-4 & 8
\end{array}\right]+\left[\begin{array}{cc}
7 & 0 \\
0 & 7
\end{array}\right]=\left[\begin{array}{ll}
0 & 0 \\
0 & 0
\end{array}\right]=O=\text { R.H.S. }
\end{aligned}
\]
More from Matrices
- 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:2025
- Given A= [-4, 4, 4; -7, 1, 3; 5, -3, -1] and B= [1, -1, 1; 1, -2, -2; 2, 1, 3], find AB. Hence, solve the system of linear equations: x-y+z=4; x-2…2025
- If a matrix A is both symmetric and skew-symmetric, then A is a:2025
- If A= [x, 0; 1, 1] and B= [4, 0; -1, 1], then value of x for which A^2=B is:2024
- If A= [1, 2, 3; 3, -2, 1; 4, 2, 1], then show that A^3-23 A-40 I=O.2023
- If [x, 2, 0] [5; -1; x] = [3, 1] [-2; x], then value of x is:2024
- If A= [0, -3, 8; 3, 0, 5; -8, -5, 0], 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 × 2. It is known…2025
CBSE Class 12 Mathematics past-paper question from the 2025 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.