The transpose of a product of matrices is the product of the transposes in reverse order.

Created almost 9 years ago, updated about 8 hours ago

For compatible matrices, $(AB)^T=B^TA^T$. The order reverses because rows become columns. Entry $ij$ on both sides is $\sum_k b_{ki}a_{jk}$. A common mistake is writing $A^TB^T$, which can even have incompatible dimensions.

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