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Question

If A is nonsingular and (A2I)(A4I)=0, then 16A+43A1 is equal to

A
0
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B
I
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C
2I
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D
6I
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Solution

The correct option is B I
Since, A is non-singular
So, A1 exists.
Given, (A2I)(A4I)=0
A26A+8I=0
Multiplying by A1, we get
A6I+8A1=0
A+8A1=6I
16A+43A1=I

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