When the ring element is homogeneous, the degrees of the source module can change, which is what makes this operation different from scalar multiplication.
i3 : QQ[x,y]
o3 = QQ[x..y]
o3 : PolynomialRing
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i4 : f = matrix "x,y"
o4 = | x y |
1 2
o4 : Matrix (QQ[x..y]) <-- (QQ[x..y])
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i5 : g = f ** y^7
o5 = | xy7 y8 |
1 2
o5 : Matrix (QQ[x..y]) <-- (QQ[x..y])
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i6 : h = f * y^7
o6 = | xy7 y8 |
1 2
o6 : Matrix (QQ[x..y]) <-- (QQ[x..y])
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i7 : degrees g
o7 = {{{0}}, {{8}, {8}}}
o7 : List
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i8 : degrees h
o8 = {{{0}}, {{1}, {1}}}
o8 : List
|