Sum of two skew symmetric matrices is always _______ matrix.

Question

Fill in the blanks:

Sum of two skew symmetric matrices is always _______ matrix.

Answer 1

A skew symmetric matrix

∴ Let A and B are two skew symmetric matrices.

⇒ A’=-A ..(1)

⇒ B’=-B ..(2)

Now Let A+B=C ..(3)

⇒ C’=(A+B)’=A’+B’

⇒ A’+B’=(-A)+(-B)

⇒ (-A)+(-B)=-(A+B)=-C

⇒ C’=-C (Skew Symmetric matrix)