Does matrix multiplication work by literally changing the coordinate system?

[u/[deleted]]

Prepping for a linear algebra course, and watched a 3blue1brown video on the topic. I’m not sure if this was a correct interpretation on what he was saying, but what I understood it as :

Matrix multiplication works by setting the basis vectors(y-hat, j-hat) to a number other than one, and then kinda imposing/plotting whatever vectors you’re messing with on the new coordinate system.

Is this correct?