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

(A). A

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.