Question

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

Answer 1

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.