a) Show that if A has a row of zeros and B is any matrix for which AB is defined, then AB also has a row of zeros.

Answer 1

Pij = term in product matrix

Pij = sum over j of Aij Bji

If Akj = 0 for some i = k and all j

Then the product row Pkj = sum over j of AkjBkj

But Akj = 0 for all j