(−2123) ( − 2 1 2 3 ) + (pqrs) ( p q r s ) = (1001) ( 1 0 0 1 ) . What is the value of r?

$\left(\begin{array}{cc}-2& 1\\ 2& 3\end{array}\right)$ + $\left(\begin{array}{cc}p& q\\ r& s\end{array}\right)$ = $\left(\begin{array}{cc}1& 0\\ 0& 1\end{array}\right)$. What is the value of r?

Answer Details

-2p + r = 1.......(i)
2p + 3r = 0.......(ii)
r - 1 + 2p ........(iii)
2p + 3(1 + 2p) = 0
2p + 3(1 + 2p) = 0
2p + 3 + 6p = 0
3 - 8p = 0 $\to$ 8p = 3
p = $\frac{3}{8}$
6 = 1 - 2 $\frac{3}{8}$
= 1 - $\frac{6}{8}$
$\frac{8-6}{8}$ = $\frac{2}{8}$
= $\frac{1}{4}$