Express the invertible matrix

$\displaystyle \left(\begin{array}{ccc}1&2&1\\1&0&1\\1&1&2\end{ar ray}\right)$

as a product of elementary matrices.

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The answer in the back of the book has a product of 6 matrices. I think I'm supposed to use the identity matrix and perform the same row operations on it as I would to obtain the above matrix... or something like that. Any help with this would be appreciated!