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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

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Solution

A-I3+A+I3-7A=A3-I3-3A2I+3AI2+A3+I3+3A2I+3AI2-7A=2A3+6AI2-7A=2A.A2+6A-7A=2A.I-A A2=I=2A-A=A

Hence, the correct option is (a).

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