Find a basis for the vector space $\lbrace A\in {\mathbb R}^{2\times 2} \mid \text{tr}(A)=0\rbrace$ of $2\times 2$ matrices with trace 0.

$B = \lbrace$ $\left[\Rule{0pt}{2.4em}{0pt}\right.$$\left]\Rule{0pt}{2.4em}{0pt}\right.$, $\left[\Rule{0pt}{2.4em}{0pt}\right.$$\left]\Rule{0pt}{2.4em}{0pt}\right.$, $\left[\Rule{0pt}{2.4em}{0pt}\right.$$\left]\Rule{0pt}{2.4em}{0pt}\right.$ $\rbrace$.