Transposing a matrix is a term for a process that "swap" the row of a matrix with its column.
All the elements within the matrix remain except for their placement.
NOTE: Matrix transpose is important and a key step in getting the Inverse matrix which is required in the solving of simultaneous equations.
The procedure to transpose is simple, but saying that, caution has to be taken of which direction to "rotate". Look carefully at the coloured elements to see the direction (below diagram).
Here you see that the symbol to represent "Transpose" s the "T" besides the original matrix. The elements remain intact and not shifted yet.
Only upon transposing, the "T" disappeared.
Now, see how the transposed elements are done.
The first row is changed to the first column, with the element "a" being the pivot point.
The pivot point (element) is taken wrongly. Normally element "c" is the target which is incorrect!
Stay focus when doing this transpose. You will then rid yourself of less trouble.
Cheers! Remember, maths is interesting! (If you are doing the correct thing.)