Inverse & Adjoint of a Matrix: JEE Questions & Solutions

For some, R, let A = pmatrix & 2 1 & 2 pmatrix and B = pmatrix 1 & 1 & 1 pmatrix be such that A^2-4A+2I-B^2-3B+I=O. Then (…

Let A be a 3 3 matrix such that A + A^T = O. If A bmatrix 1 -1 0 bmatrix = bmatrix 3 3 2 bmatrix, A^2 bmatrix 1 -1 0 bmatrix = bmatrix -3…

If X= bmatrixx bmatrix is a solution of the system of equations AX=B, where adj A= bmatrix 4 & 2 & 2 -5 & 0 & 5 1 & -2 & 3 bmatrix and B=…

Let P=[pij] and Q=[qij] be two square matrices of order 3 such that qij=2^(i+j-1)pij and (Q)=2^10. Then the value of ( adj( adj P)) is

Let A, B, C be three 2 2 matrices with real entries such that B=(I+A)^-1 and A+C=I. If BC= bmatrix1 & -5 -1 & 2 bmatrix and B bmatrixx1 2…

For a 3 3 matrix M, let trace(M) denote the sum of all the diagonal elements of M. Let A be a 3 3 matrix such that |A| = 12 and trace(A) =…

If A, B, and ( adj(A^-1) + adj(B^-1)) are non-singular matrices of the same order, then the inverse of A ( adj(A^-1) + adj(B^-1)) B is…

Let A be a 3 3 matrix such that X^TAX = 0 for all nonzero 3 1 matrices

Let A be a matrix of order 3 3 and |A| = 5. If |2 adj(3A adj(2A))| = 2^ 3^ 5^,,, N then + + is equal to

Let I be the identity matrix of order 3 3 and for the matrix A = pmatrix & 2 & 3 4 & 5 & 6 7 & -1 & 2 pmatrix, |A| = -1. Let B be the…

Let A be a 3 3 matrix such that | adj( adj A) | = 81. If S = n Z: | adj( adj A) |^ (n - 1)^22 = |A|^(3n^2 - 5n - 4), then the value of n S…

Let A = bmatrix 2 & 2 + p & 2 + p + q 4 & 6 + 2p & 8 + 3p + 2q 6 & 12 + 3p & 20 + 6p + 3q bmatrix If ( adj( adj(3A))) = 2^m 3^n, m, n N,…

Let A = bmatrix1 & 2 0 & 1 bmatrix and B = I + adj(A) + ( adj(A))^2 +... + ( adj(A))^10. The sum of all elements in B is:

Let B = bmatrix 1 & 3 1 & 5 bmatrix and A be a 2 2 matrix such that AB^-1 = A^-1. If BCB^-1 = A and C^4 + C^2 + I = O, then 2 - is equal to:

Let x, y, z 1 and A = bmatrix 1 & x y & x z y x & 2 & y z z x & z y & 3 bmatrix. Then adj(adj A^2) is equal to:

Let, then the inverse of the matrix A M^2023 A^T is:

If P is a 3 3 real matrix such that P^T = aP + (a-1)I, where a 1, then:

Let A = bmatrix 2 & 1 & 0 1 & 2 & -1 0 & -1 & 2 bmatrix. If | adj( adj( adj(2A))) | = (16)^n, then n is equal to:

Let S = M = [aij], aij 0, 1, 2, 1 i, j 2 be a sample space and A = M S: M is invertible be an event. Then P(A) is equal to:

Let 2 be the adjoint of a matrix A and |A| = 2. Then

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

Let the determinant of a square matrix A of order m be m-n, where m and n satisfy 4m+n=22 and 17m+4n=93. If (n adj(adj(mA)))=3^a5^b6^c,…