If A is a square matrix such that A^2 = I, then (A – I)^3 + (A + I)^3 – 7A is equal to

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If A is a square matrix such that A2 = I, then (A – I)3 + (A + I)3 – 7A is equal to

A. A
B. I – A
C. I + A
D. 3A

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As, (A – I)3 + (A + I)3

Use a3 + b3 = (a + b)(a2 + ab + b2)

Also A2 = I

∴ then (A – I)3 + (A + I)3 – 7A = 2A + 6A – 7A = A

Clearly our answer matches with option (A)

∴ Option (A) is the correct answer.