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If A and B are two non-zero square matrices of same order such that (A + B)² = A² + B², then :
If F(x) = [cos x –sin x 0; sin x cos x 0; 0 0 1] and [F(x)]² = F(kx), then the value of k is :
Given that [1 x][4 0; -2 0] = 0, the value of x is:
If [x 2 0][5; −1; x] = [3 1][−2; x], then value of x is :
Find the matrix A², where A = [aᵢⱼ] is a 2 × 2 matrix whose elements are given by aᵢⱼ = maximum (i, j) − minimum (i, j) :
Find the product of the matrices [1 2 −3; 2 3 2; 3 −3 −4][−6 17 13; 14 5 −8; −15 9 −1] and hence solve the system of linear equations : x + 2y − 3z = −4 2x + 3y + 2z = 2 3x − 3y − 4z = 11
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