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Question

If A=[abcd] and I=[1001], then A2(a+d)A(bcad)I=

A
0
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B
I
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C
2I
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D
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Solution

The correct option is A 0
AλI=[aIλbcdλ]
|AλI|=|aλ|(dλ)bc
=adλ(a+d)+λ2bc
=λ2λ(a+d)(bcad)
Putting A in place of λ we get
0=A2A(a+d)(bcad)

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