question_answer

Directions : (1 - 7)

The following questions consist of two statements, one labelled as "Assertion [A] and the other labelled as Reason [R]". You are to examine these two statements carefully and decide if Assertion [A] and Reason [R] are individually true and if so, whether the Reason [R] is the correct explanation for the given Assertion [A]. Select your answer from following options.

Assertion [A]: is an identity matrix.

Reason [R]: A matrix \[A=\left[ {{a}_{ij}} \right]\] is an identity matrix if .

 

A) Both A and R are individually true and R is the correct explanation of A.

B) Both A and R are individually true and R is not the correct explanation of A.

C) 'A' is true but 'R' is false

D) 'A' is false but 'R' is true

E) Both A and R are false.

Correct Answer: D

Solution :

We know that, is an indentity matrix \[\therefore \]Given Assertion [A] is false We know that for identity matrix \[{{a}_{ij}}=1,\,\,if\,\,i=j\] and       \[{{a}_{ij}}=0,\,\,if\,i\,\ne j\] \[\therefore \]Given Reason (R) is true Hence option [D] is the correct answer.