(AB)^T = (B^T*A^T) proof help

As the tittle indicates, i need help in proving the following within Matlab: (AB)^T = (B^T*A^T).

A=[1 8 5 4 ; 5 4 1 2; 4 1 2 5; 4 4 1 5],

B=[ 7 8 4 5; 7 4 5 6; 7 4 1 2; 9 4 1 2]

B and A are examples

Answer 1

[James Tursa]

Transposing in MATLAB is accomplished with the ' and .' operators. The ' operator is actually conjugate transpose and the .' is transpose without conjugate. For real inputs, ' does the same thing as .'

So for you case, replace the ^T notation with ' and then put in a * between A and B, and then you can show that the results match for any particular example.

Answer 2

[Mischa Kim]

Chris, you could simply do

 >> A = [1 8 5 4 ; 5 4 1 2; 4 1 2 5; 4 4 1 5];
 >> B = [ 7 8 4 5; 7 4 5 6; 7 4 1 2; 9 4 1 2];
 >> (A*B)' - B'*A'
 ans =
     0     0     0     0
     0     0     0     0
     0     0     0     0
     0     0     0     0

The prime does the transposing.

Answer 3

[Chris]

Wow, thankyou both very much! Both answers make clear sence and a very quick reply.