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The number of 2 × 2 matrices $A = [\begin{array}{ll} a b \\ c d \end{array}]$ or which ${[\begin{array}{ll} a b \\ c d \end{array}]}^{- 1} = [\begin{array}{cc} 1 / a & 1 / b \\ 1 / c & 1 / d \end{array}], (a, b, c, d \in R)$ is

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Correct option is A

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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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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The number of 2 × 2 matrices $A = [\begin{array}{ll} a b \\ c d \end{array}]$ or which ${[\begin{array}{ll} a b \\ c d \end{array}]}^{- 1} = [\begin{array}{cc} 1 / a & 1 / b \\ 1 / c & 1 / d \end{array}], (a, b, c, d \in R)$ is