Moment of inertia tensor is symmetric.

Moment of inertia tensor is symmetric. Why?
Ans: In linear algebra, a symmetric matrix is a square matrix A, that is equal to its transpose
i.e., A=AT
The entries of a symmetric matrix are symmetric with respect to the main diagonal (top left to bottom right). So if the entries are written as A = (aij), then aij =aji for all indices i and j. The moment of inertia tensor satisfies this condition and hence it is symmetric. (Need more details?)

K A Solaman