Question

Show that all the diagonal elements of a skew symmetric matrix are zero.

Answer 1

Answer:

To prove:All diagonal elements of a skew-symmetric matrix are all zero. Proof:Let A=[aij]n×nA=[aij]n×n be a skew symmetric matrix. ⇒aij=−aji⇒aij=−aji for all i & j. ⇒aii=−aii⇒aii=−aii (Putj=i)(Putj=i)⇒2aii=0⇒aii=0.