Chapter 4.6, Problem 46P

For Problems 45-47, a subspace $S$ of a vector space $V$ is given. Determine a basis for $S$ and extend your basis for $S$ to obtain a basis for $V$.

$V=M_2\left(ℝ\right)$, $S$ is the subspace consisting of all matrices of the form $\left[\begin{array}{cc}a& b\\ b& a\end{array}\right]$.