Question is as in title:
Why interchanging two rows of matrix results in negative determinant?
After thinking it a bit I felt:
interchanging rows = flipping orientation of transformation represented by matrix OR change orientation of space = -ve determinant / scaling factor of transformation
Q1. Is it correct?
Q2. Also is this correct for all dimensions?
Q3. How flipping orientation of vector results in 3D?
Q3. Can we say interchanging rows result in change of basis? I feel basis are still same after interchanging rows right? First row still represents x-axis despite whether we interchange values in first row with 2 nd row (y axis) or 3 rd row (z axis) etc. Does changing orientation of space is a kind of change of basis?