Solution
= Solution
{c}
Expand the <trace> by matrix entries:
$$
\operatorname{tr}(AB)=\sum_i\sum_j a_{ij}b_{ji}
=\sum_j\sum_i b_{ji}a_{ij}=\operatorname{tr}(BA).
$$
Hence \b[$\varphi(A,B)=\varphi(B,A)$]. Combined with part (a), this makes $\varphi$ a <symmetric bilinear form>.