When should you use Gauss-Jordan method to find inverse? Does the determinant only tell you whether there is an inverse?

Question

Mathematical engineering. I don't understand lol.

Answer 1

If the determinant value of a square matrix is non-zero, then said matrix does have an inverse.

 

The method of appending the identity matrix to the right of the system matrix, and performing row operations on this until that identity matrix shows up in the left half of the n by 2n augmented matrix is used, if you are required to do inversion by hand, but you have to be ever so careful!