Competition problem — Algebra — Maths Olympiad Prep

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Algebra Difficulty 5.7 AIME, harder Find the answer

4. Find the matrix $C$ such that
$C \equiv\left(\begin{array}{ll} 2 & 1 \\ 4 & 3 \end{array}\right)\left(\begin{array}{ll} 4 & 0 \\ 2 & 1 \end{array}\right)(\bmod 5)$
and all entries of $C$ are nonnegative integers less than 5 .

Your answer

A number or a short expression. Spacing and $ signs are ignored.

Solution

4. a) $\left(\begin{array}{ll}0 & 1 \\ 2 & 3\end{array}\right)$

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