Copasetic Flow

Believe it or not, I'd never really grasped that orthogonal matrices amounted to a projection into a new orthogonal coordinate system.  I have one question left about this.  If the rows of the matrix are orthogonal unit vectors, does that guarantee that the columns are?

I'm coming across several things a week in my homework and classes that are suddenly crystal clear.  These are topics that, had I gone to school in a more linear fashion, should have been clear to me three or four years ago, but now will do.  Here's the first of them, a better interpretation of matrix multiplies with column vectors.