Given the matrix \(A = \begin{vmatrix} 3 & -2 \\ 1 & 6 \end{vmatrix}\). Find the inverse of matrix A.
A. \(\begin{vmatrix} 6 & 2 \\ 1 & 6 \end{vmatrix}\)
B. \(\begin{vmatrix} \frac{2}{11} & \frac{1}{12}\\ \frac{3}{20} & \frac{1}{10} \end{vmatrix}\)
C. \(\begin{vmatrix} -3 & 2 \\ -1 & -6 \end{vmatrix}\)
D. \(\begin{vmatrix} \frac{3}{10} & \frac{1}{10} \\ \frac{-1}{20} & \frac{3}{20}\end{vmatrix}\)
Correct Answer: D
Explanation
\(A = \begin{vmatrix} 3 & -2 \\ 1 & 6 \end{vmatrix}\)
|A| = (3 x 6) - (-2 x 1)
= 18 + 2
= 20.
A\(^{-1}\) = \(\frac{1}{20} \begin{vmatrix} 6 & 2 \\ -1 & 3 \end{vmatrix}\)
= \(\begin{vmatrix} \frac{6}{20} & \frac{2}{20} \\ \frac{-1}{20} & \frac{3}{20} \end{vmatrix}\)
= \(\begin{vmatrix} \frac{3}{10} & \frac{1}{10} \\ \frac{-1}{20} & \frac{3}{20} \end{vmatrix}\)
