JEE Main Mathematics — Matrices Previous-Year Questions

Let A= [arrayll3 & -4 \ 1 & -1array ] and B be two matrices such that A¹⁰⁰=100 B+I. Then the sum of all the elements of…

If X= [arraylx \ y \ zarray ] is a solution of the system of equations A X=B, where adj A= [arrayccc4 & 2 & 2 \ -5 & 0…

Let A be a 3 × 3 matrix such that A+AT=O. If A [arrayc1 \ -1 \ 0array ]= [arrayl3 \ 3 \ 2array ], A² [arrayc1 \ -1 \ 0a…

Let A= [arrayccc0 & 2 & -3 \ -2 & 0 & 1 \ 3 & -1 & 0array ] and B be a matrix such that B(I-A)=I+A. Then the sum of the…

Let A=bmatrix 1 & 2 & 7 \ 4 & -2 & 8 \ 3 & 8 & -7 bmatrix and (A-α I)=0, where α is a real number. If the largest possi…

Let S = \A = bmatrix a & b \ c & d bmatrix : a, b, c, d \0, 1, 2, 3, 4 and A² - 4A + 3I = 0 \ be a set of 2 × 2 matrice…

Let A = bmatrix 1 & 2 \ 1 & α bmatrix and B = bmatrix 3 & 3 \ β & 2 bmatrix. If A² - 4A + I = O and B² - 5B - 6I = O, t…

Let A, B and C be three 2 × 2 matrices with real entries such that B=(I+A)⁻¹ and A+C=I. If BC= [arraycc1 & -5 \ -1 & 2a…

If A= [arrayll2 & 3 \ 3 & 5array ], then the determinant of the matrix (A²⁰²⁵-3 ~A²⁰²⁴+A²⁰²³ ) is

Let A = bmatrix 1 & 0 & 0 \ 3 & 1 & 0 \ 9 & 3 & 1 bmatrix and B = [bij], 1 ≤ i, j ≤ 3. If B = A⁹⁹ - I, then the value o…