We have seen that Sage is able to add two linear transformations, or multiply a single linear transformation by a scalar. Under the hood, this is accomplished by simply adding matrix representations, or multiplying a matrix by a scalar, according to Theorem MRSLT and Theorem MRMLT (respectively). Theorem MRCLT says linear transformation composition is matrix representation multiplication. Is it still a mystery why we use the symbol * for linear transformation composition in Sage?
We could do several examples here, but you should now be able to construct them yourselves. We will do just one, linear transformation composition is matrix representation multiplication.
Extra credit: what changes do you need to make if you dropped the side='right' option on these three matrix representations?