On bilinear complexity of multiplcation of a $3\times 2$ matrix by a $2\times 3$ matrix

It is proved that the bilinear complexity of multiplication of a $3\times 2$ matrix by a $2\times 3$ matrix is equal to $15$, over any commutative ring. In other words, the well-known Hopcroft-Kerr scheme for multiplication of such matrices is optimal, for any domain of scalars.