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Found problems: 1

2012 Centers of Excellency of Suceava, 2
Tags: abstract algebra , matrix ring , ring theory
Show that $$ \left\{ X\in\mathcal{M}_2\left( \mathbb{Z}_3 \right)\left| \begin{pmatrix} 1&1\\2&2 \end{pmatrix} X\begin{pmatrix} 1&2\\2&1 \end{pmatrix} =0 \right. \right\} $$ is a multiplicative ring. [i]Cătălin Țigăeru[/i]