How can I transpose and "untranspose" a matrix?

Question

I have this matrix:

1 2 3
4 5 6

and I transpose the matrix:

1 4
2 5
3 6

How can I get the original matrix back, after the transpose?

"untranspose" =
1 2 3
4 5 6

I am making a simple cryptographic algorithm in Java and need that to solve that problem.

Answer 1

You simply transpose the matrix again.

Description of the transposition operation properties: http://en.wikipedia.org/wiki/Transpose#Properties

Answer 2

If some linear algebra review might help, recall that U = (U^t)^t where U is your matrix and t is the symbol for the transpose operation

In short, you just flip the indices again, to get back the original matrix.

and nope... LaTeX does not work on StackOverflow :(