Given: A and B are two skew-symmetric matrices of order n Statement 1: A ⋅ B is a skew symmetric matrix when AB = - BA Let's find out transpose of (A ⋅ B) ⇒ (A ⋅ B)' = B' ⋅ A' ∵ A and B are two skew - symmetric matrices of order n i.e A' = A and B' = B ⇒ (A ⋅ B)' = B ⋅ A ⇒ (A ⋅ B)' = - (A ⋅ B)--------------(∵ AB = - BA) Hence, statement 1 is true. Statement 2: A ⋅ B is a symmetric matrix when AB = BA Let's find out transpose of (A ⋅ B) ⇒ (A ⋅ B)' = B' ⋅ A' ∵ A and B are two skew - symmetric matrices of order n i.e A' = A and B' = B ⇒ (A ⋅ B)' = B ⋅ A ⇒ (A ⋅ B)' = (A ⋅ B)--------------(∵ AB = BA) Hence, statement 2 is also true.