Matrix multiplication doesn’t work like that

Earlier this week I posted a matrix multiplication worksheet on Mastodon. If you do some of these, you might spot what’s funny about them. For example. \[ \Large \begin{bmatrix}\color{navy}{4} & \color{navy}{8}\\\color{navy}{2} & \color{navy}{3}\end{bmatrix} \begin{bmatrix}\color{cyan}{8} & \color{cyan}{8}\\\color{cyan}{2} & \color{cyan}{7}\end{bmatrix} = \begin{bmatrix}\color{navy}{4}\color{cyan}{8} & \color{navy}{8}\color{cyan}{8}\\\color{navy}{2}\color{cyan}{2} & \color{navy}{3}\color{cyan}{7}\end{bmatrix} \] That is, the answer to each question can be made…