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: A
Explanation
Let A = \(\begin{pmatrix} 4 & 2 \\ -3 & -2 \end{pmatrix}\);
|A| = -8 - (-6) = -8 + 6
|A| = -2
A\(^{-1}\) = \(\frac{1}{-2}\) = \(\begin{pmatrix} -2 & 2- \\ 3 & 4 \end{pmatrix}\)
= \(\begin{pmatrix} 1 & 1 \\ -1.5 & -2 \end{pmatrix}\)
