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A square matrix A satisfies A^2=I-A , where I is the identity matrix. If A^n =5A-3I, find the value of n.

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A square matrix A satisfies A2=I-A , where I is the identity matrix. If An =5A - 3I, find the value of n.

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The value of n will be 5

Explanation:

We know that I x A = A

A2 = I - A
A3 = A(I - A) = IA - A2 = A - (I - A) = 2A - I 
A4 = A x A3 = A(2A - I) = 2A2 -A = 2(I - A) - A = 2I - 3A
A5 = A(2I - 3A) = 2A - 3A2 = 2A - 3(I-A) = 5A - 3I

Thus, A5 = 5A - 3I

by (20 points)
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