Answer
Yes.
Work Step by Step
$\begin{bmatrix}
1& 0 \\
0&0\\
\end{bmatrix} \begin{bmatrix}
1& 0 \\
0&0\\
\end{bmatrix}= \begin{bmatrix}
1\cdot1+0\cdot0& 1\cdot0+0\cdot0 \\
0\cdot1+0\cdot0&0\cdot0+0\cdot0\\
\end{bmatrix}=\begin{bmatrix}
1& 0 \\
0&0\\
\end{bmatrix}$
Thus, the answer is yes.