Let $P=\begin{bmatrix}5 & 2\\7 & 4\end{bmatrix}, Q= \begin{bmatrix}2 & 5\\3 & 8\end{bmatrix}$ and $R= \begin{bmatrix}2 & -1\\3 & 4\end{bmatrix}$, then the matrix S such that $QS- RP= 0, $ will be :

$\begin{bmatrix}-191 & -110\\77 & 44\end{bmatrix}$

The correct answer is Option (4) → $\begin{bmatrix}-191 & -110\\77 & 44\end{bmatrix}$

$QS-RP=0$

$QS=RP$

$S=Q^{-1}RP$   [Pre-multiplying by Q]

$=\begin{bmatrix}8 & -5\\-3 & 2\end{bmatrix} \begin{bmatrix}2 & -1\\3 & 4\end{bmatrix}\begin{bmatrix}5 & 2\\7 & 4\end{bmatrix}$

$=\begin{bmatrix}-191 & -110\\77 & 44\end{bmatrix}$