This question is Exercise 1.2.20 in the book: Winfried Bruns, H. Jürgen Herzog, Cohen-Macaulay Rings, Cambridge University Press, 1998.
Let $k$ be a field and $R=k[[X]][Y]$. Deduce that $X, Y$ and $1-XY$ are maximal $R$-regular sequences.
I can not get why $1-XY$ is a maximal $R$-regular sequence. How to check the maximal condition?