In linear algebra, I learned that the reason why matrix multiplication is defined in its way is because of composition of linear transformations. So, multiplication of two matrices refers to the composition of two linear transformations.
But, when we look at a matrix representation of systems of equations, $$\ Ax = b $$ where A$A$ is a m x n$m \times n$ matrix, x$x$ is n x 1$n \times 1$ matrix of n$n$ variables, and b$b$ is m x 1$m \times 1$ matrix. We apply matrix multiplication here, but we don't refer this to the composition of linear transformations since it is a representation of systems of equations.
I'm confused about why we do matrix multiplication in the way it's defined even though it does not refer to composition of linear transformations.
