Question

If A is skew-symmetric 3*3 matrix, | A | =.....,Select Proper option from the given options.
(a) 1
(b) 0
(c) -1
(d) 3

Answer 1

skew - symmetric matrix is a type of square matrix whose transpose equals negative of it.
e.g., $A^T=-A$
for example ,
$A=\left[\begin{array}{ccc}0&a&b\\-a&0&c\\-b&-c&0\end{array}\right]$
is a skew symmetric matrix.

now, if you take determinant of A,e.g., |A|
|A| = 0(0 + c²) -a(-0 + bc) + b(ac - b)
= -abc + abc = 0

hence, if A is skew symmetric matrix then determinant of |A| is zero.

hence, option (b) is correct.