In linear algebra, the transpose of a matrix A is another matrix A ^T (also written A ′, A ^tr , ^t A or A ^t ) created by any one of the following equivalent actions:

• reflect A over its main diagonal (which runs from top-left to bottom-right) to obtain A ^T
• write the rows of A as the columns of A ^T
• write the columns of A as the rows of A ^T

Formally, the i ^th row, j ^th column element of A ^T is the j ^th row, i ^th column element of A :

[ A ^T ] _{i j} = [ A ] _{j i}

If A is an m × n matrix then A ^T is an n × m matrix.

You have been given a matrix as a 2D list with integers. ...