The (indexed) parameter R, which specifies the domain of computation, a commutative ring, must be a Maple table/module which has the following values/exports:

R[`0`] : a constant for the zero of the ring R

R[`1`] : a constant for the (multiplicative) identity of R

R[`+`] : a procedure for adding elements of R (nary)

R[`-`] : a procedure for negating and subtracting elements of R (unary and binary)

R[`*`] : a procedure for multiplying elements of R (binary and commutative)

R[`=`] : a boolean procedure for testing if two elements of R are equal

The parameters A, B, and v must have compatible dimensions for the product.

$\mathrm{with}\left(\mathrm{LinearAlgebra}\left[\mathrm{Generic}\right]\right)\:$

$Z\left[\mathrm{`0`}\right],Z\left[\mathrm{`1`}\right],Z\left[\mathrm{`+`}\right],Z\left[\mathrm{`-`}\right],Z\left[\mathrm{`*`}\right],Z\left[\mathrm{`=`}\right]≔0,1,\mathrm{`+`},\mathrm{`-`},\mathrm{`*`},\mathrm{`=`}$

$Z_0,Z_1,Z_{\mathrm{`+`}},Z_{\mathrm{`-`}},Z_{\mathrm{`*`}},Z_{\mathrm{`=`}}≔0,1,\mathrm{`+`},\mathrm{`-`},\mathrm{`*`},\mathrm{`=`}$

$A≔\mathrm{Matrix}\left(\left[\left[2\,1\,4\right]\,\left[3\,2\,1\right]\,\left[0\,0\,5\right]\right]\right)$

$A≔\left[\begin{array}{ccc}2& 1& 4\\ 3& 2& 1\\ 0& 0& 5\end{array}\right]$

$B≔\mathrm{Matrix}\left(\left[\left[1\,2\,3\right]\,\left[2\,1\,2\right]\,\left[3\,2\,1\right]\right]\right)$

$B≔\left[\begin{array}{ccc}1& 2& 3\\ 2& 1& 2\\ 3& 2& 1\end{array}\right]$

$\mathrm{MatrixMatrixMultiply}\left[Z\right]\left(A\,B\right)$

$\left[\begin{array}{ccc}16& 13& 12\\ 10& 10& 14\\ 15& 10& 5\end{array}\right]$

$v≔\mathrm{Vector}\left(\left[1\,2\,3\right]\right)$

$v≔\left[\begin{array}{c}1\\ 2\\ 3\end{array}\right]$

$\mathrm{MatrixVectorMultiply}\left[Z\right]\left(A\,v\right)$

$\left[\begin{array}{c}16\\ 10\\ 15\end{array}\right]$