Transformation of A = transpose[A] for mxn Matrices

[spybloom]

Homework Statement

"Let T:M_2,3→M_3,2 be represented by T(A) = A^T. Find the matrix for T relative to the standard bases for M_2,3 and M_3,2"

Homework Equations

I let the transformation matrix be B. I know that BA = A^T, so I need some matrix times A to equal A transpose.

The Attempt at a Solution

I'm having problems just trying to figure out the size of B. If B is 3x2, then the resultant matrix would be 3x3, which wouldn't equal the size of A^T. I've tried playing around with adding a row of zeros to the bottom of A, but then I can't figure out the contents of B. Quite frankly, I'm stumped.

 

[HallsofIvy]

I presume that you know that if you multiply an m by n matrix by an n by p matrix, you get a m by p matrix. You cannot multiply any matrix by a 3 by 2 matrix and get a 2 by 3 matrix. In order to be able to write this transformation as a matrix, you will have to write your matrices as single columns of 6 numbers.