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

A.

-\(\frac{1}{8}\)

B.

\(\frac{3}{8}\)

C.

\(\frac{5}{8}\)

D.

\(\frac{1}{4}\)

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 - \(\frac{6}{8}\)

\(\frac{8 - 6}{8}\) = \(\frac{2}{8}\)

= \(\frac{1}{4}\)