Im given that $\omega \in \Omega^3(SL(2,R))$ satisfies $\omega (I) = -2 dx_1 \wedge dx_2 \wedge dx_3$.
Consider the left multiplication $L_A(B) = AB$ as a difeormphism over $SL(2,R)$. I want to compute the pullback $L_A^*\omega (A^{-1})$.
I'm trying to use the definition of pullback $$L^*_A\omega(A^{-1})(v_1,v_2,v_3) = \omega(I) (Av_1,Av_2,Av_3)$$ but I cannot make the last calculation explictly in terms of the coordinates $x_1,x_2,x_3$ of $SL(2,R)$.
Any idea on how to proceed in this calculation. Thanks.