Romanian Matrix Problem

In this problem, I solve a neat matrix problem from a Romanian math competition, namely find all 2x2 matrices A such that A^3 - 3A^2 equals to the matrix whose entry is all -2. This is a beautiful application of linear algebra, more specifically traces and characteristic polynomials, enjoy!

Note: This problem was originally featured on blackpenredpen's channel last year, here is the link:    • A Romanian Cubic Matrix Equation  

Linear Algebra:    • Linear Algebra  
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