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Question

If A=⎡⎢⎣12101−13−11⎤⎥⎦, then


A

A3+3A2+A9I3=0

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B

A33A2+A+9I3=0

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C

A3+3A2A+9I3=0

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D

A33A2A+9I3=0

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Solution

The correct option is D

A33A2A+9I3=0


121011311A2=A.A=121011311121011311=430322645A.A2=12101131143092721117=411192721117A33A2A+9I3=0


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