Kata

When we have a 2x2 square matrix we may have up to 24 different ones changing the positions of the elements.

We show some of them

a  b   a  b    a  c    a  c   a  d    a  d    b  a    b  a
c  d   d  c    d  b    b  d   b  c    c  b    c  d    d  c

You may think to generate the remaining ones until completing the set of 24 matrices.

Given a certain matrix of numbers, that may be repeated or not, calculate the total number of possible matrices that may be generated, changing the position of the elements.

E.g: Case one

A = [[1,2,3],
     [3,4,5]]   #a 2x3 rectangle matrix with number 3 twice

generates a set of 360 different matrices

Case two

A = [[1,1,1], 
     [2,2,3], 
     [3,3,3]]

generates a set of 1260 different matrices.

Case three

A = [[1,2,3],
     [4,5,6],
     [7,8,9]]

generates a set of 362880 different matrices

This kata is not meant to apply a brute force algorithm to try to count the total amount of marices.

Features of The Random Tests

number of tests = 100
2 ≤ m ≤ 9
2 ≤ n ≤ 9

Enjoy it!

Available only in Python 2, Javascript and Ruby by the moment.