Question: Working symbolically with general/unknown matrices

Hello Y'all,

I've been on this problem for a few days now and can't seem to find a solution and hope you fine people here can help me.

Is there a way to symbolically work with matrices? In detail I'm trying to calculate blocks in a block matrix equation symbolically/analytically. The first problem I had was that of course matrices dont commutate, which is solvable by just using the LinearAlgebra package and typing in

A.B instead of A*B

For now the big problem that remains is that of course in addition to that the inversion of a matrix A is not just 1/A (or \frac{1}{A} in LaTeX) but simply A^(-1). There is the MatrixInverse function but that needs a declared matrix. And since I dont have explicit matrices I can't use Matrix or the like to declare that A is a matrix. Any help here would appreciated. I tried to work with assume, but that didn't work either and I am kind of out of options (that I find on the web) right now. In essence I just want Maple to write A^(-1) and only cancel that if an A is next to it... (albeit with not just A but of course A also being setup by addition and multiplication of matrices...).

A smaller, related interest would be a general identity matrix. One that basically just fulfills A.I=I.A=A and I^(-1)=I. At least to me that seems kind of similar but I can't just define a Mtrix as being a Matrix and not having elements...

Thank you in advance and have a nice weekend y'all! :)