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Let A and B be two symmetric matrices of order 3. Statement-1 : A(BA) and (AB)A are symmetric matrices. Statement-2 : AB is symmetric matrix if matrix multiplication of A with B is commutative. Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1. Statement-1 is true, Statement-2 is true; Statement-2 is true; Statement-2 is not a correct explanation for Statement-1. Statement-1 is true, Statement-2 is false. Statement-1 is false, Statement-2 is true.

A

Statement (1) is true and statement (2) is true and statement ( 2 ) is correct explanation for Statement (1)

B

Statement (1) is true and statement (2) is true and statement (2) is NOT a correct explanation for Statement (1)

C

Statement (1) is true but (2) is false

D

Statement (1) is false but (2) is true

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B
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MOTION-MATRICES -Exercise - 4 (Level-I)
  1. If A^2-A +I = 0, then the inverse of A is: (A) A+I (B) A (C) ...

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  2. If A=[(1,0),(1,1)] and I=[(1,0),(0,1)] , then which one of the fo...

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  3. If A and B are square matrices of order n xx n such that A^2-B^2=(A-B)...

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  4. Let {:A=[(1,2),(3,4)]and BA=[(a,0),(0,b)]:},a,b in N Then,

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  5. Let A=[5 5alphaalpha0alpha5alpha0 0 5]dot"I f"|A^2|=25 , then |alpha| ...

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  6. Let A be a 2xx2 matrix with real entries. Let I be the 2xx2 identi...

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  7. Let A be a 2xx2 matrix Statement -1 adj (adjA)=A Statement-2 abs(a...

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  8. The number of 3 3 non-singular matrices, with four entries as 1 and ...

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  9. Let A be a 2xx2 matrix with non-zero entries and let A^2=""I , whe...

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  10. If omega !=1 is the complex cube root of unity and matrix H=[(omega,...

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  11. Let A and B be two symmetric matrices of order 3. Statement-1 : A(BA) ...

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  12. Let omega!=1 be cube root of unity and S be the set of all non-singula...

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  13. Let A=((1,0,0),(2,1,0),(3,2,1)). If u(1) and u(2) are column matrices ...

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  14. Let P and Q be 3xx3 matrices with P!=Q . If P^3=""Q^3a n d""P^2Q""=""Q...

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  15. If P=[(1,alpha,3),(1,3,3),(2,4,4)] is the adjoint of a 3 x 3 matrix ...

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  16. If A is a 3 xx 3 non-singular matrix such that A A^(T) = A^(T)A " and ...

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  17. If A=[1 2 2 2 1-2a2b] is a matrix satisfying the equation AA^T=""9I , ...

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  18. If A=|{:(,5a,-b),(,3,2):}| and A adj A=A A^(T), then 5a+b is equal to

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  19. If A=|{:(,2,-3),(,-4,1):}| then adj (3A^(2)+12A) is equal to

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