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Question

Matrix A is such that A2=2AI, where I is the Identity matrix. Then for n2, An is equal to


A

nA(n1)I

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B

nAI

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C

2n+1A(n1)I

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D

2n1AI

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Solution

The correct option is A

nA(n1)I


A2=2AIA3=A2.A=(2AI)A=2A2IA=2(2AI)AA3=3A2IMultiplying with A,A4=A3.A=(3A2I)A=3A22A=3(2AI)2AA4=4A3IIn general, An=nA(n1)I


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