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If A and B are square matrices and (AB)^T (transposed) = (A^T)(B^T), is it the case that A and B commute?
Justify your answer with a proof if you say “yes” or an example that proves “no”.
Let us take a 2 x 2 square matrix to prove this:
A =
a b
c d
B =
e f
g h
(multiply the matrices above and then transpose your product)
A^T =
a c
b d
B^T =
e g
f h
(multiply the matrices above)
if they give the same answer then they are commutable.
If you need help with matrices email me.
