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Question

Suppose A is a non-singular matrix such that A3āˆ’3A2+6Aāˆ’I=0. Then, Aāˆ’1=___


A

A33A2+6A

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B

A23A+6I

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C

A2+3A6I

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D

A3+3A2+6A

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Solution

The correct option is B

A23A+6I


A33A2+6AI=0 A33A2+6A=I
Pre-multiply the equation by A1
A1A33A1A2+6A1A=A1(A1A)A23(A1A)A+6(A1A)=A1A1=A23A+6I [A1A=I]


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