If A is skew symmetric matrix of order 3 and X be another matrix of same order, then |XA + AXT| is (where |P| denotes determinant of matrix P) -
Step-by-Step Solution
Key Concept: A skew symmetric matrix of odd order has a determinant of 0. Since A is skew symmetric of order 3, |A| = 0. The expression |XA + AXT| can be simplified using properties of determinants and transpose.
Given A is a skew symmetric matrix of order 3, so AT = -A. Also, for any odd order skew symmetric matrix, |A| = 0. We need to find |XA + AXT|. Note that (XA + AXT)T = (XA)T + (AXT)T = ATXT + XAT = -AXT - XA = -(XA + AXT). This shows that (XA + AXT) is a skew symmetric matrix of order 3. The determinant of any skew symmetric matrix of odd order is 0. Therefore, |XA + AXT| = 0.
Correct Answer: 4