# Tagged: nonzero vector

## Problem 406

Let $A$ be an $n\times n$ matrix. Suppose that $\mathbf{y}$ is a nonzero row vector such that
$\mathbf{y}A=\mathbf{y}.$ (Here a row vector means a $1\times n$ matrix.)
Prove that there is a nonzero column vector $\mathbf{x}$ such that
$A\mathbf{x}=\mathbf{x}.$ (Here a column vector means an $n \times 1$ matrix.)