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If A= [[1,0],[1,1]]and I= [[1,0],[0,1]],...

If `A= [[1,0],[1,1]]and I= [[1,0],[0,1]]`, which one of the
following holds for all `n ge1`, (by the principal of
mathematical 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)I`

Text Solution

Verified by Experts

The correct Answer is:
D
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VMC MODULES ENGLISH-MATRICES AND DETERMINANTS -JEE ADVANCED ARCHIVE
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