Fill in the blanks in each of the
______ matrix is both symmetric and skew symmetric matrix.

Question

Fill in the blanks in each of the ______ matrix is both symmetric and skew symmetric matrix.

Philoid · Accepted Answer

A Zero matrix

∴ Let A be the symmetric and skew symmetric matrix.

⇒ A’=A (Symmetric)

⇒ A’=-A (Skew-Symmetric)

Considering the above two equations,

⇒ A=-A

⇒ 2A=0

⇒ A=0 (A Zero Matrix)

Hence Zero matrix is both symmetric and skew symmetric matrix.

Fill in the blanks in each of the______ matrix is both symmetric and skew symmetric matrix.