JEE Main 2023 — Matrices Questions with Solutions

If A and B are two non-zero n × n matrices such that A 2 + B = A 2 B , then

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 -…

Let A be a 3 × 3 matrix such that a d j a d j a d j . A = 12 4 . Then A - 1 a d j   A is equal to

Let A , B , C be 3 × 3 matrices such that A is symmetric and B and C are skew-symmetric. Consider the statements S…

Let A be a n × n matrix such that A = 2 . If the determinant of the matrix Adj 2 . Adj 2   A - 1 is 2 84 , th…

Let A = m n p q ,   d = A ≠ 0 and A - d Adj A = 0 . Then

Let A = 1 10 3 10 - 3 10 1 10 and B = 1 - i 0 1 , where i = - 1 . If M = A T BA , then the inverse of the matrix AM 202…

Let P be a square matrix such that P 2 = I - P . For α ,   β ,   γ ,   δ ∈ &#8…

Let A = a i ^ j ^ · a i j ∈ Z ∩ 0 , 4 ,   1 ≤ i , j ≤ 2 . The number of matrices A su…

Let for A = 1 2 3 α 3 1 1 1 2 , A = 2 . If | 2 adj ( 2 adj ( 2 A ) ) | = 32 n , then 3 n + α is equal to