Find the inverse, if it exists, for the given matrix. \[ \left[\begin{array}{ll} -3 & -1 \\ -2 & -1 \end{array}\right] \] Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The inverse matrix is . (Type a matrix, using an integer or simplified fraction for each matrix element. Do not factor out a scalar multiple.) B. There is no inverse of the given matrix.

Step 1 ：We are given the matrix A = \(\begin{bmatrix} -3 & -1 \\ -2 & -1 \end{bmatrix}\)

Step 2 ：We need to find the determinant of the matrix, which is given by the formula ad - bc. Substituting the values from the matrix, we get (-3*-1) - (-1*-2) = 1

Step 3 ：Since the determinant is not zero, the inverse of the matrix exists.

Step 4 ：We can find the inverse of the matrix using the formula \(\frac{1}{ad-bc} \begin{bmatrix} d & -b \\ -c & a \end{bmatrix}\). Substituting the values from the matrix and the determinant, we get \(\frac{1}{1} \begin{bmatrix} -1 & 1 \\ 2 & -3 \end{bmatrix}\)

Step 5 ：So, the inverse of the matrix A is \(\begin{bmatrix} -1 & 1 \\ 2 & -3 \end{bmatrix}\)

Step 6 ：\(\boxed{\begin{bmatrix} -1 & 1 \\ 2 & -3 \end{bmatrix}}\) is the final answer.