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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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  4. Let A be the set of all 3xx3 skew-symmetri matrices whose entries are ...

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  6. Let S be the set which contains all possible vaues fo I ,m ,n ,p ,q ,r...

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  7. If A is a diagonal matrix of order 3xx3 is commutative with every squa...

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  8. If A is a square matrix of order 3 such that |A|=2,t h e n|(a d jA^(-1...

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  9. If A and B are two matrices of order 3 such that AB=O and A^(2)+B=I, t...

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  10. If a, b, and c are integers, then number of matrices A=[(a,b,c),(b,c,a...

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  11. Let A=[a("ij")] be 3xx3 matrix and B=[b("ij")] be 3xx3 matrix such tha...

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  12. A square matrix M of order 3 satisfies M^(2)=I-M, where I is an identi...

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  13. Let A=[a("ij")](3xx3), B=[b("ij")](3xx3) and C=[c("ij")](3xx3) be any ...

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  14. If A is a square matrix of order 2xx2 such that |A|=27, then sum of th...

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  15. If A is a aquare matrix of order 2 and det. A=10, then ((tr. A)^(2)-tr...

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  16. Let A and B are two square matrices of order 3 such that det. (A)=3 an...

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  17. Let P, Q and R be invertible matrices of order 3 such A=PQ^(-1), B=QR^...

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  18. If A=[(1,x,3),(1,3,3),(2,4,4)] is the adjoint of a 3xx3 matrix B and d...

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  19. A, B and C are three square matrices of order 3 such that A= diag. (x,...

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  20. Let A=[a("ij")] be a matrix of order 2 where a("ij") in {-1, 0, 1} and...

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