Why does the y-axis of one of my objects appear to be backwards? My Transform Orientation is set to local. I have this object that when highlight is using a right hand co-ordinate system (z up, x forward, y orthogonal to the x-z plane):



I click on another object and the transform looks like this:



Which is not right handed. How do I reset this object to use right handed coordinates? I'm not sure what I did to make it like this. It's like the Y axis is backwards. Any ideas?
You have a negative scale - see the Scale panel on the right-hand side. Press Ctrl-A and Apply Scale and the transform should behave as you expect. You may also need to Recalculate Normals once you've applied the scale in case any are left pointing in the wrong direction.