# Matrix multiplication in Block Form symbolic calculation by Mathematica

I have a problem which requires taking product of two $10\times10$ matrices. I would like to do it by considering both matrices as $5\times5$ matrices such that each entry of both matrices is actually a $2\times2$ matrix; moreover, there are variables so this is a symbolic calculation. (Side remark: matrix multiplication is not a commutative operation, i.e. $AB\neq BA$ in general.) Does anyone know how to perform this block form multiplication in Mathematica, or using any other software?

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