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Question

If B=52α1021α31 is the inverse of a 3×3 matrix A, then the sum of all values of α for which det(A)+I=0, is

A
2
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B
1
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C
0
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D
1
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Solution

The correct option is B 1
As B is the inverse of matrix A
Therefore det(A)=1det(B)det(B)=5(23)+α(2α2) =2α22α25
Also det(A)+1=0
α2α12=0
α=4,3
Sum=43=1

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