Hard Lin Alg.
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"
If A were invertible then
Originally Posted by caeder012
Would that matrix necessarily have zero entries?