Statement-1 (Assertion and Statement- 2 (Reason)
Each of these questions also has four alternative
choices, only one of which is the correct answer. You
have to select the correct choice as given below.
Statement - 1 If A is skew-symnmetric matrix of order 3,
then its determinant should be zero.
Statement - 2 If A is square matrix,
`det (A) = det (A') = det (-A')`

Options

A. Statement-1 is true, Statement -2 is true, Statement-2
is a correct explanation for Statement-1
B. Statement-1 is true, Statement-2 is true, Sttatement - 2
is not a correct explanation for Stamtement-1
C. Statement 1 is true, Statement - 2 is false
D. Statement-1 is false, Statement-2 is true

Answer

C

Explanation

Statement -2 is false
`because det (A^(-1)) ne det (-A')`
`[because det (-A')=(-1)^(3) det (A') = - det(A') ]`
but in Statement-1
`A'=-A rArr A = -A'`
`therefore det(A) = det(-A')`
`=- det A' = - det (A)`
`rArr 2 det (A) = 0`
` therefore det (A) = 0`
Then, Statement - 1 is true.