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. Your task is to return a transposed matrix based on input.

Input: A matrix as a list of lists with integers.

Output: The transposed matrix as a list/tuple of lists/tuples with integers.

Example:

checkio([[1, 2, 3],
         [4, 5, 6],
         [7, 8, 9]]) == [[1, 4, 7],
                         [2, 5, 8],
                         [3, 6, 9]])
checkio([[1, 4, 3],
         [8, 2, 6],
         [7, 8, 3],
         [4, 9, 6],
         [7, 8, 1]]) == [[1, 8, 7, 4, 7],
                         [4, 2, 8, 9, 8],
                         [3, 6, 3, 6, 1]])

How it is used: The most obvious use for this idea is in mathematical software, but the concept can be applied in the area of vector graphics. On a computer, one can often avoid explicitly transposing a matrix in memory by simply accessing the same data in a different order.

Precondition:
0 < len( matrix ) < 10
all(0 < len(row) < 10 for row in matrix )