$\begin{pmatrix} -2 & 1 \\ 2 & 3 \end{pmatrix}$ $\begin{pmatrix}p & q \\ r & s\end{pmatrix}$ = $\begin{pmatrix} 1 & 0 \\0 & 1 \end{pmatrix}$ . What is the value of r?

- $\frac{1}{8}$

$\frac{3}{8}$

$\frac{5}{8}$

$\frac{1}{4}$

Correct answer is D

-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 - $\frac{6}{8}$

$\frac{8 - 6}{8}$ = $\frac{2}{8}$

= $\frac{1}{4}$

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