Let A and B be nx n matrices. Show that if the ith row of A has all zero entries, then the ith row of AB will have all zero entries. Let A = [a;] and B = [b¡j] be two diagonal nxn matrices. Then the ijth entry of the product AB is n Σ Cij = k = 1 If the ith row of A has all zero entries, evaluate the entries aik for all k = 1, 2, ..., n. aik = Evaluate the entries C¡¡ for all j = 1, 2, ..., n. Cij = Thus, if the ith row of A has all zero entries, then the ith row of AB has all zero entries. Give an example using 2 x 2 matrices to show that the converse is not true. 1 2 B = 3 4 14 18 B =

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