Maths-
General
Easy

Question

Assertion : If A is a skew symmetric of order 3 then its determinant should be zero.
Reason : If A is square matrix then det A = det straight A to the power of straight prime = det (–straight A to the power of straight prime)

  1. If both (A) and (R) are true, and (R) is the correct explanation of (A).    
  2. If both (A) and (R) are true but (R) is not the correct explanation of (A).    
  3. If (A) is true but (R) is false.    
  4. If (A) is false but (R) is true.    

The correct answer is: If (A) is true but (R) is false.


    The reason R is false since
    det straight A to the power of straight prime= det (–straight A to the power of straight prime) is not true.
    Indeed det (–straight A to the power of straight prime) = (–1)3 det straight A to the power of straight prime
    Now as A = –straight A to the power of straight prime (A is skew symmetric)
    det A = det (–straight A to the power of straight primenot stretchy rightwards double arrow –det (straight A to the power of straight primenot stretchy rightwards double arrow – det A
    not stretchy rightwards double arrow det A = 0
    The assertion A is true.

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