Directions : Questions are Assertion- Reason type questions. Each of these questions contains two statements :

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.

Question : Let A be a  2 x 2 matrix

Statement-1 : adj\, (adj\; A)=A

Statement-2 : \left |adj\; A \right |=\left | A \right |

 

 

  • Option 1)

    Statement-1 is true,Statement-2 is true; Statement-2 is not a correct explanation for Statement-1

  • Option 2)

    Statement- 1 is true, Statement-2 is false

  • Option 3)

    Statement-1 is false, Statement-2 is true

  • Option 4)

    Statement-1 is true, Statement-2 is true; Statement-2 is correct explanation for Statement-1

 

Answers (2)

As we learnt in 

Property of adjoint of A -

\left | adj A \right |=\left | A \right |^{n-1}  

- wherein

adj A denotes adjoint of A and  \left |A \right |  denotes determinant  of A and n is the order of the matrix

 

 |adjA|= |A|^{n-1}= |A|^{2-1}= |A|      Statement 2 is true

adj|adjA|= |A|^{n-2}A= |A|^{0}A= A  Statement 1 is true

 


Option 1)

Statement-1 is true,Statement-2 is true; Statement-2 is not a correct explanation for Statement-1

Correct Option

Option 2)

Statement- 1 is true, Statement-2 is false

Incorrect Option

 

Option 3)

Statement-1 is false, Statement-2 is true

Incorrect Option

 

Option 4)

Statement-1 is true, Statement-2 is true; Statement-2 is correct explanation for Statement-1

Incorrect Option

 

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