Answer
$|A|=1$
$\begin{array} \\A^{-1}=\\ \end{array}
\begin{bmatrix} 9&-4\\ -2&1 \end{bmatrix}$
Work Step by Step
Step 1. List the matrix needed:
$\begin{array} \\A=\\ \end{array}
\begin{bmatrix} 1&4\\ 2&9 \end{bmatrix}$
Step 2. Calculate the determinant: $|A|=1\times9-4\times2=1$
Step 3. Calculate $A^{-1}$ (use the formula from section 10.5):
$\begin{array} \\A^{-1}=\\ \end{array}
\frac{1}{1\times9-4\times2}\begin{bmatrix} 9&-4\\ -2&1 \end{bmatrix}
=\begin{bmatrix} 9&-4\\ -2&1 \end{bmatrix}$
