Question

All the diagonal entries of a skew symmetric matrix are positive.

• A. True
• B. False

Answer 1

The correct option is B

False

For a skew symmetric matrix we know that A = $-A^T$ i.e., aij = (aji) x (-1)

Or aij = -aji……………..(1)

Now the diagonal elements are represented by aii i.e.for i= j $a_{ij}$becomes the diagonal element.

For diagonal elements (1) becomes aii = -aii or 2aii = 0 or aii = 0 i.e. diagonal elements are zero for a skew symmetric matrix.

Hence the statement is False.