Question

how do I show the cross product of two vectors, transformed under an inversion, has opposite direction in new coordinates. I see that by the RHR it would, but with matrices, I am not getting the anomaly.

Answer 1

Or should I be looking for a contradiction example. The actual problem is to identify how the cross product transforms under an inversion.
\[x_{1}=-x, y_{1}=-y, z_{1}=-z\]