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