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If A is a square matrix such that A2 = I, then find the simplified value of (A – I)3 + (A + I)3 – 7A. - Mathematics

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 If A is a square matrix such that A2 = I, then find the simplified value of (A – I)3 + (A + I)3 – 7A.

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Solution

Given:

(AI)3+(A+I)37A

=A3I33A2I+3AI2+A3+I3+3A2I+3AI27A

2A3+6AI27A

=2A.A2+6AI27A

=8A7A

=A

Concept: Types of Matrices
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