How to find the order of a matrix?

[xsw001]

For example the Heisenberg group over Field.

H(F) is a 3x3 upper right triangle where the entries on the main diagonals are all 1's.

So by definition that I need to use this matrix and raise to the power where it becomes the identity matrix, then the number of that power would the order of H(F). But if I take the upper right triangle with all 1's in the main diagonal, it would never becomes identity matrix though no matter how many times I multiple them.

I couldn't find any examples from the material that I have. Am I doing something wrong here? Any suggestions?

 

[Tinyboss]

If you have $$g^m\ne1$$ for every positive integer m, you say that g has infinite order.