Question

Mark each of the following statement true or false: If A and B are matrices such that AB = O and A neq O, then B = O.

Matrices
ANSWERED
asked 2021-01-13
Mark each of the following statement true or false: If A and B are matrices such that AB = O and \(A \neq O\), then B = O.

Answers (1)

2021-01-14
Step 1
Given statement,
If A and B are matrices such that AB = O and \(A \neq O\), then B = O.
Step 2
Take A and B to be two matrices
\(A=\begin{bmatrix}1 & 0 \\0 & 0 \end{bmatrix}\neq 0 \text{ and } B=\begin{bmatrix}0 & 0 \\1 & 0 \end{bmatrix}\)
\(AB=\begin{bmatrix}1 & 0 \\0 & 0 \end{bmatrix}\begin{bmatrix}0 & 0 \\1 & 0 \end{bmatrix}\)
\(AB=\begin{bmatrix}0 & 0 \\0 & 0 \end{bmatrix} \text{ and } A=\begin{bmatrix}1 & 0 \\0 & 0 \end{bmatrix} \neq 0\)
But B is non Zero.
Therefore, the given statement is false.
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