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

Expansion of the given expression,

A³ – I³ + 3AI² – 3A²I + A³ + I³ + 3AI² + 3A²I – 7A

2A³ – 7A + 6AI²

2A²A – 7A + 6A

2AI – A {A² = I}

2A – A

A

Option (A) is the answer.