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Question
If A is a square matrix such that A2 = A, find the value of 7A – (I + A)3
Solution
Given A2 = A
So 7A – (I + A)3
= 7A – (I + 3A + 3A2 + A3)
= 7A – I – 3A – 3 A2 – A3
Given A2 = A
7A – I – 3A – 3A – A3
= – I + A – A3
= – I + A – (A2 × A)
= – I + A – (A × A)
= – I + A – A2
= – I + A – A = -I
So the value of 7A – (I + A)3 = – I.
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