A square matrix $A$ is called half-magic if the sum of the numbers in each row and column is the same. The common sum in each row and column is denoted by $s(A)$ and is called the magic sum of the matrix $A$. Let $V$ be the vector space of $2\times 2$ half-magic squares.
(a) Find an ordered basis $B$ for $V$.
$B = ($ $\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.$ $)$.
(b) Find the coordinate vector $[M]_B$ of $M=\left[\begin{array}{cc} -6 &1\cr 1 &-6 \end{array}\right]$ in your chosen ordered basis $B$.
$[M]_B =$ $\left[\Rule{0pt}{2.4em}{0pt}\right.$$\left]\Rule{0pt}{2.4em}{0pt}\right.$.