Which of the following statement('s) is/are TRUE?
(A) Skew symmetric matrix of even order is always symmetric
(B) Skew symmetric matrix of odd order is non-singular
(C) Skew symmetric matrix of odd order is singular
(D) Skew symmetric matrix is always square matrix
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (C) and (D) only
Consider the properties of a skew-symmetric matrix $A$:
(i) $A^T = -A$
(A) Skew-symmetric matrix of even order is always symmetric → False, because $A^T = -A \neq A$ unless $A = 0$.
(B) Skew-symmetric matrix of odd order is non-singular → False, determinant of skew-symmetric matrix of odd order is always 0, so it is singular.
(C) Skew-symmetric matrix of odd order is singular → True.
(D) Skew-symmetric matrix is always square → True, because transpose is defined only for square matrices in $A^T = -A$.