sha 3 - What criteria make the theta step of Keccak's round function reversible?

From what I've been reading, Keccak's round function is reversible. That's pretty obvious for the $\rho$, $\pi$ and $\iota$ transforms. For $\chi$ to be reversible, $x$'s range has to be odd — but that's alright since Keccak's $x$ has a range of 5. Yet, what criteria make the theta step reversible?Checking some small $x$, $y$ and $z$ ranges, it shows that:where [x][y][z]'s ranges are [3][3][2], $\theta$ is not reversible, and where [x][y][z]'s ranges are [3][3][3], $\theta$ is not reversible either. So, what makes the $\theta$ for (eg) [5][5][...Read more