A square matrix is half-magic if the sum of the numbers in each row and column is the same. Find a basis $B$ for the vector space of $2\times 2$ half-magic squares.

$B = \lbrace$ $\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.$ $\rbrace$.