# Theory of complexity – Counting on a matrix.

I have a $$n times m$$ matrix, and fill it with numbers $$1 sim k$$

If a matrix can be converted into another matrix by exchanging its lines and exchanging its columns, it is considered that the two matrices are the same.

I know that I can easily calculate the numbers of the different matrices in $$O ((n times m) ^ k)$$ time, but is there any other better algorithm for these problems?

I also wonder if $$texttt {Burnside's motto}$$ or $$texttt {Polya's Theorem}$$work here I'm not having ideas with them.