Show that it is not always true that AB = A^T B^T for matrices A, B.

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Show that it is not always true that AB = A^T B^T for matrices A, B.

Mathematics
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To disprove something, you merely need to provide a counterexample. Pick any two arbitrary matrices, of any size. I picked [1 2] and [1 3] [0 1] and [0 1] Transposing them you get [1 0] and [1 0] [2 1] [3 1] Do the math yourself to verify it; you should get [1 5] vs [1 0] [0 1] [4 1] Clearly they are not equal.

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