If $\left[\begin{array}{ll}2 & 1 \ 3 & 2\end{array} ight] A\left[\begin{array}{cc}-3 & 2 \ 5 & -3\end{array} ight]=\left[\begin{array}{ll}1 & 0 \ 0 & 1\end{array} ight]$, then $A=$

Question

If $\left[\begin{array}{ll}2 & 1 \ 3 & 2\end{array}ight] A\left[\begin{array}{cc}-3 & 2 \ 5 & -3\end{array}ight]=\left[\begin{array}{ll}1 & 0 \ 0 & 1\end{array}ight]$, then $A=$

Aicharya · Accepted Answer

$\begin{aligned} & {\left[\begin{array}{ll}2 & 1 \ 3 & 2\end{array}ight] A\left[\begin{array}{cc}-3 & 2 \ 5 & -3\end{array}ight]=\left[\begin{array}{ll}1 & 0 \ 0 & 1\end{array}ight]} \ & \Rightarrow A=\left[\begin{array}{ll}2 & 1 \ 3 & 2\end{array}ight]^{-1}\left[\begin{array}{ll}1 & 0 \ 0 & 1\end{array}ight]\left[\begin{array}{ll}3 & 2 \ 5 & 3\end{array}ight]^{-1} \ & \Rightarrow A=\left[\begin{array}{cc}2 & -1 \ -3 & 2\end{array}ight]\left[\begin{array}{ll}1 & 0 \ 0 & 1\end{array}ight]\left[\begin{array}{ll}3 & 2 \ 5 & 3\end{array}ight] \ & \Rightarrow A=\left[\begin{array}{cc}2 & -1 \ -3 & 2\end{array}ight]\left[\begin{array}{ll}3 & 2 \ 5 & 3\end{array}ight] \ & \Rightarrow A=\left[\begin{array}{ll}1 & 1 \ 1 & 0\end{array}ight]\end{aligned}$

If $\left[\begin{array}{ll}2 & 1 \\ 3 & 2\end{array}\right] A\left[\begin{array}{cc}-3 & 2 \\ 5 &…

Solution