Practice Test 10

Let $A$ be a $2 \times 3$ matrix and $B$ be a $2 \times 2$ matrix:

$$A=\begin{bmatrix}1&0&2\-1&3&4\end{bmatrix},\quad B=\begin{bmatrix}2&-1\0&5\end{bmatrix}.$$

Given the matrices above, why is the operation $AB$ not defined?

Let $A$ and $B$ be $2\times 2$ matrices:

$$A=\begin{bmatrix}3&0\-1&2\end{bmatrix},\quad B=\begin{bmatrix}1&4\2&-3\end{bmatrix}.$$

Given the matrices above, which statement about $AB$ and $BA$ is true?