Q.

The number of 2 × 2 matrices A=a    bc    d or which a    bc    d−1=1/a1/b1/c1/d,(a,b,c,d∈R) is

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a

0

b

1

c

2

d

infinite

answer is A.

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Detailed Solution

If ad−bc≠0 thenA−1=1ad−bcd−b−caThus, dad−bc=1a⇔ad=ad−bc⇔bc=0⇔b=0 or c=0Therefore,a    bc    d−1=1/a    1/b1/c    1/dis never possible.
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