Transpose of a matrix product
= Transpose of a matrix product
{title2=$(AB)^T=B^TA^T$}
For compatible finite <matrices>, the <transpose> reverses the factor order. Entrywise, $[(AB)^T]_{ij}=\sum_kA_{jk}B_{ki}=\sum_k(B^T)_{ik}(A^T)_{kj}$, proving the identity. The analogous formula for <conjugate transpose> is $(AB)^\dagger=B^\dagger A^\dagger$. Commutativity of scalar entries permits the last rearrangement; the matrix products themselves are not assumed to <commute>.