Which of the following statements are True or False
If A is skew symmetric matrix, then A² is a symmetric matrix.

Question

Which of the following statements are True or False If A is skew symmetric matrix, then A 2 is a symmetric matrix.

Philoid · Accepted Answer

True

For skew symmetric matrix A’=-A

⇒ (A²)’=(AA)’=A’A’

⇒ A’A’=(-A)(-A)=A²

⇒ (A²)’=A² (symmetric matrix)

Which of the following statements are True or FalseIf A is skew symmetric matrix, then A2 is a symmetric matrix.