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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 :
If A = [1 0 2; 0 2 1; 2 0 3], then show that A³ − 6A² + 7A + 2I = O.
For two matrices A and B, given that A⁻¹ = (1/4)B, then inverse of (4A) is :
If A = [[1, 3], [3, 4]] and A² – kA – 5I = O, then the value of k is :
If A = [–3 –2 –4; 2 1 2; 2 1 3] and B = [1 2 0; –2 –1 –2; 0 –1 1], then find AB and use it to solve the following system of equations : x – 2y = 3 2x – y – z = 2 –2y + z = 3
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