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Question
If A is a square matrix such that A2 = I, then find the simplified value of (A – I)3 + (A + I)3 – 7A.
Solution
Given:
(A−I)3+(A+I)3−7A
=A3−I3−3A2I+3AI2+A3+I3+3A2I+3AI2−7A
= 2A3+6AI2−7A
=2A.A2+6AI2−7A
=8A−7A
=A
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