Question

What is the product?

Answer 1

`=\begin{pmatrix}-5&6\\ 1&-4\end{pmatrix}`

Explanation:

`\begin{pmatrix}-3&4\\2&-5\end{pmatrix}\begin{pmatrix}3&-2\\ 1&0\end{pmatrix}`

Multiply the row of the first matrix to the column of the second matrix

`\begin{pmatrix}-3&4\end{pmatrix}\begin{pmatrix}3\\ 1\end{pmatrix}=\left(-3\right)\cdot \:3+4\cdot \:1`

`\begin{pmatrix}-3&4\end{pmatrix}\begin{pmatrix}-2\\ 0\end{pmatrix}=\left(-3\right)\left(-2\right)+4\cdot \:0`

`\begin{pmatrix}2&-5\end{pmatrix}\begin{pmatrix}3\\ 1\end{pmatrix}=2\cdot \:3+\left(-5\right)\cdot \:1\`

`\begin{pmatrix}2&-5\end{pmatrix}\begin{pmatrix}-2\\ 0\end{pmatrix}=2\left(-2\right)+\left(-5\right)\cdot \:0\`

`=\begin{pmatrix}\left(-3\right)\cdot \:3+4\cdot \:1&\left(-3\right)\left(-2\right)+4\cdot \:0\\ 2\cdot \:3+\left(-5\right)\cdot \:1&2\left(-2\right)+\left(-5\right)\cdot \:0\end{pmatrix}`

simplifying them we get

`=\begin{pmatrix}-5&6\\ 1&-4\end{pmatrix}`