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8 matrix multiplication is associative, so you can do it in whichever order you like I'm not sure why it would take so long to compute. You can prove it by writing the matrix multiply in summation notation each way and seeing they match.

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First multiply all elements of the $i$th row of the matrix $a$ pairwise with all the elements of the $j$th column of the matrix $b$ Which should do the correct thing And then you add these $n$ products.

Matrix multiplication is defined so that it works right to left, just like function composition

This allows matrices to represent linear transformations more intuitively The eventual coefficients obtained from a double transformation of (x, y, z) require row elements of the left transform matrices to be multiplied by their corresponding column element of the right. Is $a a^\\mathrm t$ something special for any. The sum of matrices corresponds to the transformation which is the sum of the two given transformations

Addition of linear transformations require the domain and range to be. Multiply on the left is usually called premultiply, while multiply on the right is usually called postmultiply. The standard manner i would use to multiply matrices is the dot operator