Question

If A=$\left[\begin{array}{cc}a& b\\ c& d\end{array}\right]$, then $A^{-1}$ = [MP PET 1988]

• A.
• B.
• C.
• D. None of these

Answer 1

The correct option is A

$A^{-1}$ = $\frac{adjA}{|A|}$

But, |A| =$\left[\begin{array}{cc}a& b\\ c& d\end{array}\right]$ = ab - cd and adj A =$\left[\begin{array}{cc}b& -c\\ -d& a\end{array}\right]$

Therefore, $A^{-1}$ = $\frac{1}{ab-cd}$ $\left[\begin{array}{cc}b& -c\\ -d& a\end{array}\right]$