About maximum length of matrix can be use for matrix invertsion on atmega32
Floats in the Arduino IDE are normally 4 bytes. So you can work out with a calculator that your matrix will take at least 15 x 15 x 4 bytes (900 bytes). That is out of a total of 2048 bytes of RAM on the Atmega32.
That may seem to be enough RAM, but other things, like the libraries, will also take RAM. I did an answer to a question about RAM a while back. Even a very simple sketch (in this case) took 346 bytes.
Also, your library, or whatever-it-is you are using for matrix inversion, may require RAM for variables, etc.
My suggestion would be to make your code invert a very small matrix (eg. 1 x 1) and see how much RAM that uses. Then you can extrapolate out fairly simply to how much would be needed for a larger matrix.