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Statement-1 (Assertion and Statement- 2 ...

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 mateix `A= [a_(ij)] _(3xx3) , B= [b_(ij)] _(3xx3), ` where ` a_(ij) + a_(ji) = 0 and b_(ij) - b_(ji) = 0` then `A^(4) B^(5)` is non-singular
matrix.
Statement-2 If A is non-singular matrix, then `abs(A) ne 0 .`

A

Statement- 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

Text Solution

Verified by Experts

The correct Answer is:
D
Since, matrix A is skew-symmetric
`therefore abs(A) = 0`
` therefore abs(A^(4) B^(5)) = 0`
`rArr A^(4) B^(5)` is singular matrix.
Statement-1 is false and Statement - 2 is true.
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Knowledge Check

  • If matrix A = [a_(ij)]_(3xx3), matrix B= [b_(ij)]_(3xx3) where a_(ij) + a_(ij)=0 and b_(ij) - b_(ij) = 0 then A^(4) cdot B^(3) is

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  • If matrix A=[a_(ij)]_(3xx) , matrix B=[b_(ij)]_(3xx3) , where a_(ij)+a_(ji)=0 and b_(ij)-b_(ji)=0 AA i , j , then A^(4)*B^(3) is

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