Now we know that invertibility is equivalent to nonsingularity, and that the procedure outlined in Theorem CINM will always yield an inverse for a nonsingular matrix. But rather than using that procedure, Sage implements a .inverse() method. In the following, we compute the inverse of a $3\times 3$ matrix, and then purposely convert it to a singular matrix by replacing the last column by a linear combination of the first two.
Notice how the failure to invert C is explained by the matrix being singular.
Systems with nonsingular coefficient matrices can be solved easily with the matrix inverse. We will recycle A as a coefficient matrix, so be sure to execute the code above.
If you find it more convenient, you can use the same notation as the text for a matrix inverse.