Find the inverse of  \(\begin{pmatrix} 4 & 2 \\ -3 & -2 \end{pmatrix}\)

A.

\(\begin{pmatrix} 1 & 1 \\ -1.5 & -2 \end{pmatrix}\)

B.

\(\begin{pmatrix} 1 & -1 \\ 1.5 & -2 \end{pmatrix}\)

C.

\(\begin{pmatrix} -2 & 1 \\ 1.5 & 1 \end{pmatrix}\)

D.

\(\begin{pmatrix} -2 & -1 \\ 1.5 & 1 \end{pmatrix}\)

Correct answer is A

Let A =  \(\begin{pmatrix} 4 & 2 \\ -3 & -2 \end{pmatrix}\);

|A| = -8 - (-6) = -8 + 6

|A| = -2

A\(^{-1}\) = \(\frac{1}{-2}\) =  \(\begin{pmatrix} -2 & 2- \\ 3 & 4 \end{pmatrix}\)

= \(\begin{pmatrix} 1 & 1 \\ -1.5 & -2 \end{pmatrix}\)