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`.

Options

A. Statement - 1 is true, Statement - 2 is true , Statement - 2
is correct explanaction for Statement -2
B. Statement -1 is true, Statement - 2 is true, Statement - 2
is not a correct explanation for Statement-2
C. Statement-1 is true, Statement-2 is false
D. Statement-1 is false, Statement-2 is ttrue

Answer

B

Explanation

`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.