Find the inverse matrix for the given matrix. \[ \begin{array}{l} {\left[\begin{array}{cc} -14 & -13 \\ -9 & -8 \end{array}\right]} \\ A^{-1}=? \end{array} \]

Step 1 ：We are given the matrix A = \(\begin{bmatrix} -14 & -13 \\ -9 & -8 \end{bmatrix}\)

Step 2 ：The inverse of a 2x2 matrix \(\begin{bmatrix} a & b \\ c & d \end{bmatrix}\) is given by \(\frac{1}{ad-bc} \begin{bmatrix} d & -b \\ -c & a \end{bmatrix}\)

Step 3 ：First, we need to calculate the determinant (ad-bc) of the given matrix. The determinant of matrix A is -4.999999999999988

Step 4 ：Since the determinant of the matrix A is not equal to zero, the matrix is invertible

Step 5 ：Applying the formula for the inverse of a 2x2 matrix, we get the inverse of the matrix A as \(\begin{bmatrix} 1.6 & -2.6 \\ -1.8 & 2.8 \end{bmatrix}\)

Step 6 ：Final Answer: The inverse of the given matrix is \(\boxed{\begin{bmatrix} 1.6 & -2.6 \\ -1.8 & 2.8 \end{bmatrix}}\)