Show that if,

A= \left(\begin{array}{cc}1 & 0\\0 & 0 \end{array}\right)

B =  \left(\begin{array}{cc}0 & 0\\0 & 1 \end{array}\right)

C =  \left(\begin{array}{cc}0 & 1\\1 & 0 \end{array}\right)

Then span of {A,B,C} is the set of all symmetric 2x2 matrices