How do I find relationships between $$ lk(L),\; lk(mL),\; lk(rL),\; lk\Big(m \big(r(L)\big)\Big),$$ for any arbitrary oriented link $L$, where $m$ denotes the mirror and $r$ denotes the reverse.
So far I have found the linking number 'lk' for a certain knots but don't know how to generalise it. With the diagrams I've drawn I found that $lk(L)=lk(rL)$ and $lk(mL)=lk(m(r(L)))$ but does this hold for any arbitrary oriented link?