If $A=\left[\begin{array}{cc}3 & -1 \ -4 & 2\end{array} ight]$, then $A^{-1}$ is

Question

If $A=\left[\begin{array}{cc}3 & -1 \ -4 & 2\end{array}ight]$, then $A^{-1}$ is

Aicharya · Accepted Answer

$\begin{aligned} A= & {\left[\begin{array}{cc}3 & -1 \ -4 & 2\end{array}ight] } \ A^{-1}= & \frac{1}{6-4}\left[\begin{array}{ll}2 & 1 \ 4 & 3\end{array}ight] \ & \ldots\left[	ext { If } A=\left[\begin{array}{ll}a & b \ c & d\end{array}ight] 	ext { and } a d-b c 
eq 0, 	ext { then }ight. \ = & \left.\frac{1}{2}\left[\begin{array}{ll}2 & 1 \ 4 & 3\end{array}ight] \quad A^{-1}=\frac{1}{(a d-b c)}\left[\begin{array}{cc}d & -b \ -c & a\end{array}ight] .ight] \ A^{-1}= & {\left[\begin{array}{ll}1 & \frac{1}{2} \ 2 & \frac{3}{2}\end{array}ight] }\end{aligned}$

If $A=\left[\begin{array}{cc}3 & -1 \\ -4 & 2\end{array}\right]$, then $A^{-1}$ is

Solution