Matrix X is such that X 2-2 X - I- where I is identity matrix- then for n - 2- X n is equal toA- n X-n-1 IB- n X - IC- 2 n X - n -1 ID- 2n X-I

The correct option is A nX (n 1)IX^2 = 2X I ⇒ X^3 = 2X^2 X=3X 2I X^4 = 4X 3I …… X^n=nX (n 1)I ...

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Equality of Matrices

Matrix X is s...

Question

Matrix X is such that $X^{2} = 2 X - I$ , where I is identity matrix, then for $n \geq 2, X^{n}$ is equal to

n X - (n - 1) I

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n X - I

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

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2^{n} X - I

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Solution

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Similar questions

A

A^{2} = 2 A - I

I

n \geq 2

A^{n}

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

n \in N; A^{n}

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