# How do I calculate variations of a square matrix if the elements are binary?

I have a 3x3 square matrix. I want to find out how many unique matrices I can create if each of the elements can be either 1 or 0.

How does the equation change if have NxN matrix?

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Unique according to what measure? You mean uniqueness up to equivalence under similarity transformations $A=S^{-1}BS$? – Raskolnikov Jan 11 '11 at 15:34
Sorry I incorrectly labeled this question. Its actually an array, not a matrix. – mtully Jan 11 '11 at 16:36

If you have 2 choices for each of 9 positions in the matrix, there are 2^9 different possibilities. And if there are N^2 positions,...

Is the matrix just an array of numbers, or is there more structure to the problem?

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This is what I was looking for, 2^(N*N). It is just an array. Thanks! – mtully Jan 11 '11 at 16:27