Home
Class 12
MATHS
Statement-1 (Assertion) and Statement- 2...

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 as given below.
Statement-1 if A and B are two square matrices of order
`nxxn` which satisfy `AB= A and BA = B,` then
`(A+B) ^(7) = 2^(6) (A+B)`
Statement- 2 A and B are unit matrices.

A

Statement- is true, Statement -2 is true, Statement-2
is a correct explanation for Statement-2

B

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

C

Statement 1 is true, Statement - 2 is false

D

Statement-1 is false, Statement-2 is true

Text Solution

Verified by Experts

The correct Answer is:
C
`because AB = A, BA = B rArr A^(2) = A and B^(2) = B`
`therefore (A+B) ^(2) = A^(2) + B^(2) + AB + BA = A + B + A +B`
` = 2(A+B)`
`(A+B)^(3) = (A+B) ^(2) . (A+B)`
`=2 (A+B)^(2) = 2^(2) (A+B)`
`therefore (A+B)^(7) = 2^(6) (A+B)`
Statement - 1 is true and Statement -2 is false.
Promotional Banner

Similar Questions

Explore conceptually related problems

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 matrices, then A^(2) = A, B^(2) = B .

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 as given below. Statement- 1 If A, B, C are matrices such that abs(A_(3xx3))=3, abs(B_(3xx3))= -1 and abs(C_(2xx2)) = 2, abs(2 ABC) = - 12. Statement - 2 For matrices A, B, C of the same order abs(ABC) = abs(A) abs(B) abs(C).

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 select the correct choice as given below. Statement-1 If p,q in N satisfy the equation x^sqrtx=(sqrtx)^x and qgtp , then q is a perfect number . statement 2 If a number is equal to the sum of its factor, then number is known as perfect number.

If A and B are two square matrices of the same order , then AB=Ba.

Select the correct statement from the ones given below

If A and B are square matrices of same order then (A^(-1)BA)^(n) = ………… , n inN .

If A, B are symmetric matrices of same order, then AB-BA is a

If A and B are symmetric matrices of same order , then AB +BA is a ……