Nice job multiplying those matrices. But you did not prove that AC is "an inverse matrix". That doesn't make sense because what matrix would AC be the inverse of?? Notice it has only 1s on the diagonal which makes it an IDENTITY matrix. The definition of the inverse matrix is a matrix that turns another matrix into an identity matrix (when you multiply them). Thus, by showing that A*C = an identity matrix, you proved that C is the inverse matrix of A. (C turns A into an identity matrix)

This is similar to the idea of a "multiplicative inverse" which turns a number into 1 when you multiply. For example the "multiplicative inverse" of 2 is 1/2 because 2 * (1/2) = 1.