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Let , be a 2x2 matrix where . The number of such matrices which have inverse is
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a
5
b
6
c
7
d
8
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Correct option is B
det(A)=ad−bcNote that det(A) can take value –1, 0 or 1. We havedet(A)=1⇔ad=1,bc=0⇔a=1,d=1 or (b=0,c=0,b=0;c=1b=1,c=0)and det(A)=−1⇔ad=0 or bc=1This is also possible in 3 cases.∴ A−1 exists in 6 cases.Similar Questions
If , then is
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