If matrix A such that A2 - 2A - I- where I is the identity matrix- then for n -2- where n- N- An is equal to

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Equality of Matrices

If matrix A...

Question

If matrix $A$ such that $A^{2} = 2 A - I$ , where $I$ is the identity matrix, then for $n \geq 2$ , where $n \in N; A^{n}$ is equal to

n A - (n - 1) I

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n A I

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2^{n - 1} A - (n - 1) I

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2^{n - 1} A - I

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Matrix A is such that $A^{2} = 2 A - I,$ where I is the Identity matrix. Then for $n \geq 2, A^{n}$ is equal to

A

A^{2} = 2 A - I

I

n \geq 2

A^{n}

A^{2}

(I + A)^{n}

If A = (\begin{matrix} 1 & 0 1 & 1 \end{matrix}] and I = (\begin{matrix} 1 & 0 0 & 1 \end{matrix}], then which of the following holds for all n \in N ?

A

A^{2} = 2 A - 1

l

n \geq 2, A^{n}

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