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matrix equation

Source: Romanian District Olympiad 2000, Grade XI, Problem 1

September 24, 2018
linear algebramatrixcontestsromaniaalgebra

Problem Statement

Solve in the set of 2×2 2\times 2 integer matrices the equation X2−4⋅X+4⋅(1emsp;00emsp;1)=(7emsp;812emsp;31). X^2-4\cdot X+4\cdot\left(\begin{matrix}1  0\\0  1\end{matrix}\right) =\left(\begin{matrix}7  8\\12  31\end{matrix}\right) .
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