Given $\left[\begin{array}{cc}1& 2\\ 3& 4\end{array}\right]\left[\begin{array}{cc}3& 1\\ 2& 5\end{array}\right]$ = $\left[\begin{array}{cc}7& 11\\ \mathit{k}& 23\end{array}\right]$
Now using matrix multiplication in LHS, we get
= $\left[\begin{array}{cc}7& 11\\ \mathit{k}& 23\end{array}\right]$
⇒ $\left[\begin{array}{cc}3+4& 1+10\\ 9+8& 3+20\end{array}\right]$ = $\left[\begin{array}{cc}7& 11\\ \mathit{k}& 23\end{array}\right]$
⇒ $\left[\begin{array}{cc}7& 11\\ 17& 23\end{array}\right]$ = $\left[\begin{array}{cc}7& 11\\ \mathit{k}& 23\end{array}\right]$
Now on equating the corresponding elements we get the value of k = 17