Short question about key of Hill Cipher

Question

Is the key of Hill cipher for example for $m=2$, the determinant always an odd number?

Because when I try to make a key and the determinant is even number, I can't find the inverse in modulo 26.

Answer 1

The determinant must be odd and not 13. This is because of the fact that a matrix with entries mod $n$ is invertible if and only if its determinant is invertible mod $n$. Since the only invertible elements mod 26 are the odds except 13, the same must be required of your determinant.