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

Question

Philoid · Accepted Answer

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.

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