In linear algebra, the transpose of a matrix A is another matrix A^T (also written A′, A^tr,^tA 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)