In questions determine whether the statement is true or false.
-$$\text { If } \mathbf { A } \text { and } \mathbf { B } \text { are } 2 \times 2 \text { matrices such that } \mathbf { A B } = \left( \begin{array} { l l }
0 & 0 \
0 & 0
\end{array} \right) \text {, then } \mathbf { A } = \left( \begin{array} { l l }
0 & 0 \
0 & 0
\end{array} \right) \text { or } \mathbf { B } = \left( \begin{array} { l l }
0 & 0 \
0 & 0
\end{array} \right) \text {. }$$

Question

In questions determine whether the statement is true or false.
-$$\text { If } \mathbf { A } \text { and } \mathbf { B } \text { are } 2 \times 2 \text { matrices such that } \mathbf { A B } = \left( \begin{array} { l l } 
0 & 0 \
0 & 0
\end{array} \right) \text {, then } \mathbf { A } = \left( \begin{array} { l l } 
0 & 0 \
0 & 0
\end{array} \right) \text { or } \mathbf { B } = \left( \begin{array} { l l } 
0 & 0 \
0 & 0
\end{array} \right) \text {. }$$

Quizplus · Accepted Answer

The product of two non-zero matrices can be the zero matrix if they are singular and their null spaces align appropriately.

In Questions Determine Whether the Statement Is True or False