# Transformation of A = transpose[A] for mxn Matrices

1. Dec 1, 2011

### spybloom

1. The problem statement, all variables and given/known data
"Let T:M2,3→M3,2 be represented by T(A) = AT. Find the matrix for T relative to the standard bases for M2,3 and M3,2"

2. Relevant equations
I let the transformation matrix be B. I know that BA = AT, so I need some matrix times A to equal A transpose.

3. 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 AT. 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.

2. Dec 2, 2011

### HallsofIvy

Staff Emeritus
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.