Question

Let A have a row all of whose entries are zero. Explain why the product AB also has a zero row.

Answer 1

Reason is Matrix Multiplication Technique

Explanation:

Matrix Multiplication: In matrix multiplication each element of a row is multiplied with each element of a column. So, row with all its zero entries is multiplied with all of the columns and making corresponding entries as zeros as well.

Therefore, A with a row having all zero entries also produces a row with all zero entries during multiplication with any matrix B.