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Question

Matrix A is such that A2=2A1 where 1 is the unit matrix Then for n2, An=

A
nA(n1)I
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B
nAI
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C
2n+1A(n1)I
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D
2n+1A1
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Solution

The correct option is B nA(n1)I
A2=2A1
An=An2A2
=An2(2A1)
=2An1An2
A22A+I=0
(AI)=0
A=I
An=I
Put in all options only (A) comes out I

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