The matrix $$A=\left[\begin{array}{ccc} -2 &0 &1\cr 2 &-1 &-2\cr -1 &0 &0 \end{array}\right]$$ has one real eigenvalue. Find this eigenvalue and a basis of the eigenspace.

The eigenvalue is .

A basis for the eigenspace is $\Bigg\lbrace$ $\left[\Rule{0pt}{3.6em}{0pt}\right.$$\left]\Rule{0pt}{3.6em}{0pt}\right.$, $\left[\Rule{0pt}{3.6em}{0pt}\right.$$\left]\Rule{0pt}{3.6em}{0pt}\right.$ $\Bigg\rbrace.$