Question

Show that if A is a matrix with a row of zeros (or a column of zeros), then A cannot have an inverse

Answer 1

As per the question,

Matrix have row zero,

$=\begin{bmatrix} 0 & 0 & 0\\ a &b & c\\ d &e & f\\ \end{bmatrix}$

to prove A is singular we must show that there is no 3x3 matrix B, such that B.A = I

For this purpose, let 0, R1, and R2 be the row vector of A.

Hence, for any 3x3 matrix, B can be express the product B.A

BA= I