If $В$ is an arbitrary member of the inner product space, show that $L_b$ is unitarily equivalent to $R_{B^t}$.

Question

Let $V$ be the space of complex $n \times n$ matrices equipped with the inner product $<A,B> = tr (AB^*). $

If $В$ is an element of $V$, let $L_b, R_b$ denote the linear operators on $V$
defined by $(a)$ $L_B(A) = BA$. $(b) R_B(A) = AB$.

If $В$ is an arbitrary member of the inner product space, show that $L_B$ is unitarily equivalent to $R_{B^t}$.

To prove this we have to find a matrix $U$ such that $UL_BU^* =R_{B^t}$.

I am not getting any clue to this...please Help!