[Math] Find $XY$ given matrix $YX$ where $X$ is a row matrix and $Y$ is a column matrix

matrices

I've been given matrix $YX$ as below. I want to find $XY$ from it. I know that $X$ is a row matrix and $Y$ is a column matrix. $X$ has $2$ entries and $Y$ has $2$ entries. However I don't know the values of each entry.

$$YX=
\begin{bmatrix}
-2 & -3 \\
2 & 3
\end{bmatrix}$$

I'm not quite sure how to progress from here. I know that the result will be one number. I'd like some guidance on where to go next.

Best Answer

Hint: $$\begin{bmatrix}a \\ b\end{bmatrix}\times\begin{bmatrix}c & d\end{bmatrix}= \begin{bmatrix}ac & ad \\ bc & bd\end{bmatrix}$$

Then: $$\begin{bmatrix}c & d\end{bmatrix}\times\begin{bmatrix}a \\ b\end{bmatrix}= \begin{bmatrix}ac +bd\end{bmatrix}$$

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