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A square matrix M of order 3 satisfies M...

A square matrix M of order 3 satisfies `M^(2)=I-M`, where `I` is an identity matrix of order 3. If `M^(n)=5I-8M`, then `n` is equal to _______.

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Verified by Experts

The correct Answer is:
6
`M^(3)=M^(2)M=(I-M)M=M-M^(2)=2M-I`
Similarly,
`M^(4)=2I-3M`
`M^(5)=5M-3I`
`M^(6)=%I-8M`
`:. n=6`
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