Orthogonal, Idempotent, Nilpotent and Involutory Matrices

JEE Main Mathematics · Matrices and Determinants · 6 questions, latest first

• Let A= [0, 2, -3; -2, 0, 1; 3, -1, 0] and B be a matrix such that B(I-A)=I+A. Then the sum of the diagonal elements of B^T B is…202623 January, Shift 2 · Q21
• Let A=I_2-2 M M^T, where M is a real matrix of order 2 × 1 such that the relation M^T M=I_1 holds. If λ is a real number such…20241 February, Shift 2 · Q21
• Let A be a square matrix such that AA^T=I. Then 1/2 A[(A+A^T)^2+(A-A^T)^2] is equal to202429 January, Shift 1 · Q4
• Let P= [(√3)/2, 1/2; -1/2, (√3)/2], A= [1, 1; 0, 1] and Q=P A P^T. If P^T Q^2007 P= [a, b; c, d], then 2 a+b-3 c-4 d equal to20238 April, Shift 1 · Q5
• Let A=[a_i j]_2 × 2, where a_i j ≠ 0 for all i, j and A^2=I. Let a be the sum of all diagonal elements of A and b=|A|. Then 3…20236 April, Shift 1 · Q3
• Let A= [1/(√10), 3/(√10); -3/(√10), 1/(√10)] and B= [1, -i; 0, 1], where i=√-1. If M=A^T B A, then the inverse of the matrix A…202325 January, Shift 2 · Q64