What is the trace of the second tensor component?

Question

My teacher asks to prove that for any matrix $A \in \operatorname{Mat}(N, \mathbb{C})$ there is true: $$ A=\operatorname{tr}_2\left(P_{12} A_2\right) $$ where $A_{2}=E_{N}\otimes A$ and $P_{12}$ is permutation operator for tensor components: $$P_{12}A_{2}=A\otimes E_{N}=A_1$$ but I don't understand what is $tr_2$ and there is no any mentions of it in the internet. The teacher only says that it is the trace of the second tensor component, but it doesn't help.