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**Software for multiplication of matrices**

I'm going to do a lot of matrix multiplications, since I'm computing Jarlskog invariants. I would like to know if there is a great program for doing a lot of matrix multiplications? I tried with Maple but at some point it gives up. My matrices are not very large: 3x3 or 2x2, but the elements get quite complicated, since I do matrix multiplication of 8 matrices.

I do not have access to Mathematica, but would that be a possibility?

MATLAB seems complicated, since I'm using functions and letters.

I think someone talked about that Latex could do computations?

What are your suggestions? :)