Final answer:
The determinant of a matrix is important to find before finding the inverse because it helps identify singular matrices.
Step-by-step explanation:
The determinant of a matrix is important to find before finding the inverse because it helps identify singular matrices. A singular matrix is one that does not have an inverse. By finding the determinant first, we can determine if the matrix is singular or not. If the determinant is zero, then the matrix is singular and does not have an inverse. If the determinant is non-zero, then the matrix is non-singular and has an inverse. This step is crucial because trying to find the inverse of a singular matrix would result in an error or an undefined solution.
For example, consider the 2x2 matrix:
[a b]
[c d]
The determinant of this matrix is ad - bc. If the determinant is zero, it means that the matrix is singular and does not have an inverse. If the determinant is non-zero, the inverse exists and can be found by swapping the diagonal elements, changing the sign of the off-diagonal elements, and dividing by the determinant. In this case, the inverse of the matrix would be:
[d -b]
[-c a]