question_answer

Assertion [A]: For two matrices and \[{{\left( A+B \right)}^{2}}={{A}^{2}}+2AB+{{B}^{2}}\].

Reason [R]: For given two matrices A and B, AB = BA.

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: A

Solution :

Given \[\Rightarrow \,\,AB=BA\]. Now \[{{\left( A+B \right)}^{2}}=\left( A+B \right)\,\left( A+B \right)\] \[=\text{ }{{A}^{2\text{ }}}+AB+BA+{{B}^{2}}\] \[=\text{ }{{A}^{2}}+AB+AB+{{B}^{2}}\] \[\left\{ \because \,\,AB=BA \right\}\] \[=\text{ }{{A}^{2}}+\text{ }2AB+{{B}^{2}}\] \[\therefore \]Given Assertion [A] is true Also \[AB=BA\Rightarrow \]Reason (R) is true and is correct explanation of A Hence option [A] is me correct answer.