Trace and transpose of a Matrix

Question

I have a recurrence relation as follows

$ \left\{ \begin{array}{ll} R_0=H & \mbox{if } n = 0 \\ R_1 =sR_0 \hspace{.1cm} A & \mbox{if }n=1\\ R_{n+2} =\frac{s}{n+2}\{ R_{n+1} \hspace{.1cm}A+ s\hspace{.1cm} R_{n} \hspace{.1cm}B\} & \mbox{if }n>= 2\\ \end{array} \right. \tag 1$

And we have defined $R =\sum_{n=0}^{\infty} R_n \tag 2$ This is a converging series

Specifications

1. H,A,B are constant matrices with dimension $3 \times 3$ and s is a constant

2. R has dimension $ 3 \times 3$

3. A,B are skew symmetric matrices with determinant $0$

4. H is a rotation 3D matrix. Implies orthogonal and determinant 1

5. $$A=\left( \begin{array}{ccc} 0 & -c_0 & b_0 \\ c_0 & 0 & -a_0 \\ -b_0 & a_0 & 0 \\ \end{array} \right).$$ $$B=\left( \begin{array}{ccc} 0 & -(c_1-c_0) & (b_1-b_0) \\ (c_1-c_0) & 0 & -(a_1-a_0) \\ -(b_1-b_0) & (a_1-a_0) & 0 \\ \end{array} \right).$$

   NB: All entries of the matrices $A$, $B$ are constants,can't be altered

Question

How can we find as a finite result following expressions

1. $Trace(R )$
2. $R -R ^T$