Question

Inverse matrix of $\left[\begin{array}{cc}4& 7\\ 1& 2\end{array}\right]$ is equal to:

• A. $\left[\begin{array}{cc}2& -7\\ -1& 4\end{array}\right]$
• B. $\left[\begin{array}{cc}2& -1\\ -7& 4\end{array}\right]$
• C. $\left[\begin{array}{cc}-2& 7\\ 1& -4\end{array}\right]$
• D. $\left[\begin{array}{cc}-2& 1\\ 7& -4\end{array}\right]$

Answer 1

Answer: (A)

Let $A=\left[\begin{array}{cc}4& 7\\ 1& 2\end{array}\right]$
$|A|=8-7=1$
Cofactors of $A$ are $C_{11}=2,C_{12}=-1$
$C_{21}=-7,C_{22}=4$
$\therefore adj(A)=\left[\begin{array}{cc}2& -7\\ -1& 4\end{array}\right]$
$\therefore A^{-1}=\frac{adj(A)}{|A|}=\frac{1}{1}\left[\begin{array}{cc}2& -7\\ -1& 4\end{array}\right]$
If a matrix, $A=\left[\begin{array}{cc}a& b\\ c& d\end{array}\right]$,
then $adj(A)=\left[\begin{array}{cc}d& -b\\ -c& a\end{array}\right]$ .