Answer
See below
Work Step by Step
Assume that $A=\begin{bmatrix}
1 & 0\\
1 & 1
\end{bmatrix}$
with eigenvalues $\lambda_A=1$
$B=\begin{bmatrix}
1 & 1\\
0 & 1
\end{bmatrix}$
with eigenvalues $\lambda_B=1$
So $\lambda_A=\lambda_B=1$
Obtain $A-B=\begin{bmatrix}
0 & 1\\
-1 & 0
\end{bmatrix}$
We can see $\lambda_{A-B}\ne0$
Hence, the statement is not true.
