Suppose we have two matrices, matrix A and matrix B, both of which are 5x5 matrices. Further, suppose that all the entries in A and B are nonzero. However, the third column in the PRODUCT of AB is all zero.

1.) Can matrix A be invertible? If so, give an example. If not, justify why not.

2.) Can matrix B be invertible? If so, give an example. If not, justify why not.

We were given this hint:

"Consider what the definition of the product AB of 2 matrices means"