Dot and wedge products

DotPr2[a_, b_] := 1/2 (Mul2[a, b] + Mul2[b, a])

Simplify[DotPr2[avec, bvec]]//MatrixForm

( {{ax bx + ay by}, {{0, 0}}, {0}} )

Wedge2[a_, b_] := 1/2 (Mul2[a, b] - Mul2[b, a])

Simplify[Wedge2[avec, bvec]]//MatrixForm

( {{0}, {{0, 0}}, {-ay bx + ax by}} )


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