Question
Show that $(A B)^T=A^T B^T$ if and only if $A$ and $B$ are square commuting matrices.
Step 1
Generally, for any matrices \(A\) and \(B\) (where the dimensions are such that \(AB\) is defined), the transpose of the product is given by: \[ (AB)^T = B^T A^T \] This is a standard result in linear algebra. Show more…
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