looking for the inverse of matrix that has to be use RREF, and also it needs to be in modulo 5, is there a more straight forward way to do this?

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Trying to do it step by step with RREF operations but I'm not making any progress, is there any more straight forward way to do this?

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In $\mathbb Z_5$, it holds $2\cdot 3=1$ and $4\cdot 4=1$. Using this information, you can divide by any number, and proceed with the usual algorithm.