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If A is a square matrix such that A^(2)=...

If A is a square matrix such that `A^(2)= I`, then
`(A-I)^(3)+(A+I)^(3)-7A` is equal to

Text Solution

Verified by Experts

We have, `A^(2)=I`
Now, a and I are commutative.
`(A-I)^(3)+(A+I)^(3)-7A`
`=A^(3)-3A^(2)I+3AI+3AI-I^(3)+A^(3)+3A^(2)I+3AI+I^(3)-7A`
`=2A^(3)+6A-7A`
`=2A^(2)xxA-A=2IxxA-A=2A-A=A`
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