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If A=[(1,0),(1,1)] and I=[(1,0),(0,1)] t...

If `A=[(1,0),(1,1)] and I=[(1,0),(0,1)]` then which one of the following holds for all `nge1` by the principle of mathematica induction? (A) `A^n=2^(n-1) A+(n-1)I` (B) `A^n=nA+(n-1) I` (C) `A^n=2^(n-1) A-(n-1)I` (D) `A^n=nA-(n-1) AI`

A

`A^(n)=nA+(n-1)I`

B

`A^(n)=nA-(n-I)I`

C

`A^(n)=nA-(n-1)I`

D

`A^(n)=(2n-1)A-(n-1)I`

Text Solution

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The correct Answer is:
C
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