If A = [1 0 2; 0 2 1; 2 0 3], then show that A³ − 6A² + 7A + 2I = O.

Question

TextMatrix Multiplication and Its ConditionsProperties of Matrix MultiplicationCBSE PYQ

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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 :

Matrix Multiplication and Its Conditions

Properties of Matrix Multiplication

If A = [2 1; -4 -2], then the value of I – A + A² – A³ + ... 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) :