If A is \(2\times 3\) and B is \(3\times 4\), state the size of \(AB\).

Compute \(\begin{pmatrix}1&2\\3&4\end{pmatrix}\)\(\begin{pmatrix}5\\6\end{pmatrix}\).

Compute \(\begin{pmatrix}2&0\\-1&3\end{pmatrix}\)\(\begin{pmatrix}4&1\\2&-2\end{pmatrix}\).

Compute \(AB\) for \(A=\begin{pmatrix}1&0&2\\-1&3&1\end{pmatrix}\) and \(B=\begin{pmatrix}2&1\\0&4\\5&-2\end{pmatrix}\).

For \(A=\begin{pmatrix}1&2\\0&1\end{pmatrix}\) and \(B=\begin{pmatrix}3&0\\4&5\end{pmatrix}\), compute \(BA\).

Show that matrix multiplication is not commutative for \(A=\begin{pmatrix}1&1\\0&1\end{pmatrix}\) and \(B=\begin{pmatrix}1&0\\1&1\end{pmatrix}\).

Let A be \(3\times 2\), B be \(2\times 5\), and C be \(5\times 4\). State the size of \(ABC\).

Find x if \(\begin{pmatrix}x&1\end{pmatrix}\)\(\begin{pmatrix}2\\3\end{pmatrix}\) = \(\begin{pmatrix}11\end{pmatrix}\).

A learner computes \(\begin{pmatrix}1&2&3\end{pmatrix}\)\(\begin{pmatrix}4&5&6\end{pmatrix}\) by multiplying entries position by position. Explain why this is not a valid matrix product.

For \(A=\begin{pmatrix}1&2\\3&4\end{pmatrix}\), compute \(A^2\), meaning AA.