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Lets say I want to factorize [tex]

\begin{bmatrix}

1 & a & a+1 \\

a+1 & 1 & a \\

a & a+1 & 1

\end{bmatrix}[/tex]

Where should I start? Is there a general way to do this so that the process is a bit quick especially for when it comes to exams? Thanks!