InterviewSolution
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InterviewSolution
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Statement -1 (Assertion) and Statement - 2 (Reason) Each of these examples 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 A and B are two matrices such that AB = B, BA = A, then ` A^(2) + B^(2) = A+B.` Statement-2 A and B are idempotent motrices, then `A^(2) = A, B^(2) = B`.A. Statement - 1 is true, Statement - 2 is true , Statement - 2 is correct explanaction for Statement -2B. Statement -1 is true, Statement - 2 is true, Statement - 2 is not a correct explanation for Statement-2C. Statement-1 is true, Statement-2 is falseD. Statement-1 is false, Statement-2 is ttrue |
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Answer» Correct Answer - B `because AB = B` `rArr B(AB) = B cdot B` `rArr (BA) B = B^(2) ` [ "by associative law"] `rArr AB = b^(2) [ because BA=A]` `rArr B= B^(2) [because AB=B]` and Ba = A `rArr A(BA) = A cdot A` `rArr (AB) A + A^(2) ` [by associative law] `rArr BA= A^(2) " " [because AB=B]` `rArr A=A^(2) [ because BA=A]` Hence, `therefore A^(2) + B^(2) = A + B` Here, both statments are true and Statement - 2 is not a correct explanation for Statement-1. |
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