I don't know how to prove this if and only if statement.
Let A & B be symmetric matrices.
Show AB is symmetric if and only if AB=BA.
Any help is much appreciated!
I got that...but I don't know how to express this.
Ok, I know in an if and only if proposition, then you have to prove the statement both ways (forwards and backwards).
So....Assume AB is symmetric. Show AB=BA
(AB)^T=(B^T)(A^T). We know A & B are symmetric so,
AB=BA
Then you have to go the other way...
Assume AB=BA, show AB is symmetric.
So do I do the same this basically as before to show this?
(AB)^T=(B^T)(A^T)=BA
Thanks.