Matrix calculation and calculus in general form

Can Mathematica do the followings? (Note that dimension of matrices are given by general parameters like $m,n$)

1. Can it do matrix calculation in general form? For example solving the following equation $XA=B$ where $A,B$ are matrix and $X$ is a vector. The solution is $X=A^{-1}B$. The goal is basically to derive some equations in general form. If it cannot do that, any form of Collect function can be useful. At least being able to collect the following expression with respect to $X$: $2X+AX$ (a formula like Collect$[2X+AX,X]$). The answer should be $(2+A)X$
2. Can Mathematica do matrix calculus as well? For example taking derivative with respect to $X$ for $X’AX$ for which the answer is $(A+A’)X$

Note that I prefer a general form. One might for example define the matrix by $A=[a_{11},a_{12},…]$, but then the inverse would be a messy expression.

if these are not possible is there any other software which can do something like that?