Question

If a matrix is both symmetric and skew symmetric, then it is a ______________ matrix

Answer 1

If a matrix is both symmetric and skew symmetric matrix, then it is a null matrix.

Proof :-

For a symmetric matrix

A = Á

and, for a skew symmetric matrix

A = - Á .

This both equality holds simultaneously when each element of the matrix will be zero.

Regards

Kshitij

Answer 2

Answer:

If a matrix is both symmetric and skew symmetric, then it is a zero matrix