- #1

Mr Davis 97

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## Homework Statement

Let ##A## be an ##n \times n## matrix. Show that if ##A^2## is the zero matrix, then the only eigenvalue of ##A## is 0.

## Homework Equations

## The Attempt at a Solution

All eigenvalues and eigenvectors must satisfy the equation ##A\vec{v} = \lambda \vec{v}##. Multiplying both sides by ##A##, we have that ##A \vec{v} = \vec{0}##. In this the correct direction? I am not sure where to go from here...