Principal Axes

An axis through which the product of moment of area is $0$. $$

$$I_{xy} = 0$$

There will be 2 principal axes which are perpendicular to each other.

If a plane area has more than 2 axes of symmetries, all centroidal axes will be principal centroidal axes. In such case, second moment of area with respect to any centroidal axis will be a constant.

Principal second moments of area

Second moments about the principal axes.

About principal axes second moments of area will be at minimum and maximum.

Centroidal principal axes

Principal axes through the centroid. An axis of symmetry is a centroidal principal axis.