The given matrix P is a projection matrix. A projection matrix satisfies P² = P. Let's verify this property for the given matrix.

Given P = $\left[\begin{array}{cc}1& 0\\ 0& 0\end{array}\right]$. Compute P² = P × P = $\left[\begin{array}{cc}1& 0\\ 0& 0\end{array}\right]$ × $\left[\begin{array}{cc}1& 0\\ 0& 0\end{array}\right]$ = $\left[\begin{array}{cc}1& 0\\ 0& 0\end{array}\right]$ = P. Since P² = P, it is indeed a projection matrix.

Final Answer: $\left[\begin{array}{cc}1& 0\\ 0& 0\end{array}\right]$