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A^2=0 if A^3=0 for 2x2 real matric A

Source: 1990 Greece MO Grade XII p1

September 6, 2024

linear algebramatrix

Problem Statement

Let

A

be a

2\,x\,2

matrix with real numbers. Prove that if

A^3=\mathbb{O}

then

A^2=\mathbb{O}