documentclass{article}
usepackage{luacode}
begin{luacode}
function MatMul( m1, m2 )
    if #m1[1] ~= #m2 then
        return nil
    end

    local res = {}

    for i = 1, #m1 do
        res[i] = {}
        for j = 1, #m2[1] do
            res[i][j] = 0
            for k = 1, #m2 do
                res[i][j] = res[i][j] + m1[i][k] * m2[k][j]
            end
        end
    end

    for i = 1, #res do
    for j = 1, #res[1] do
        tex.sprint( res[i][j] )
        tex.sprint("  ")
    end
    tex.sprint("n")
end
end
newcommandmatrixmult[2]{directlua{MatMul(#1,#2)}}

begin{document}
matrixmult{{ { 1, 2, 4 }, { 4, 5, 6 } }}{{ { 1, 2 }, { 3, 4 }, { 5, 6 } }}
end{document}

documentclass{article}
usepackage{luacode}
begin{luacode}
function MatMul( m1, m2 )
    if #m1[1] ~= #m2 then
        return nil
    end

    local res = {}

    for i = 1, #m1 do
        res[i] = {}
        for j = 1, #m2[1] do
            res[i][j] = 0
            for k = 1, #m2 do
                res[i][j] = res[i][j] + m1[i][k] * m2[k][j]
            end
        end
    end

    for i = 1, #res do
    for j = 1, #res[1] do
        tex.sprint( res[i][j] )
        tex.sprint("  ")
    end
    tex.sprint("\par")
end
end
end{luacode}
newcommandmatrixmult[2]{directlua{MatMul(#1,#2)}}

begin{document}
matrixmult{{ { 1, 2, 4 }, { 4, 5, 6 } }}{{ { 1, 2 }, { 3, 4 }, { 5, 6 } }}
end{document}