Let $T:V\rightarrow W$ be a linear transformation, and $T^*:W^*\rightarrow V^*$ the dual transfomation, which is defined by $T^*(f):=f \ \circ T$ for every linear functional $f\ \in W^*$.
$C{w}:W\rightarrow W^{**}$ and $C{v}:V\rightarrow V^{**}$ are the canonical isomorphisms.
Prove if V,W are finite, then $(T^*)^* \circ C_{v} = C_{w}\circ T$.
I tried to set bases and dual bases, but couldn't get further.
Any ideas?