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If A and B are square matrices of the sa...

If A and B are square matrices of the same order such that `(A+B)(A-B)=A^(2)-B^(2)`, then `(ABA)^(2)=`

A

Either of A or B is zero matrix

B

A=B

C

AB=BA

D

Either of A or B is an identity matrix

Text Solution

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The correct Answer is:
C
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Knowledge Check

  • If A and B are square matrices of the same order, then

    A
    `A+B=B+A`
    B
    `A+B=A-B`
    C
    `A-B=B-A`
    D
    `A B=B A`

  • If A and B are square matrices of same order such that, (A+B)^2=A^2+B^2+2 AB , then

    A
    `AB=BA`
    B
    `A=B`
    C
    ` A=B^prime`
    D
    `A=-B`

  • If A and B are two square matrices of same order then (A B)^(prime)=

    A
    `B^(prime) A^(prime)`
    B
    A' B'
    C
    `A B^(prime)`
    D
    `A^(prime) B`

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    Explore conceptually related problems

    If A and B are invertible matrices of same order then prove that (AB)^(-1) = B^(-1)A^(-1)

    If A and B are symmetric matrices , then ABA is :

    If A and B are two square matrices of the same order such that AB=B and BA=A , then A^(2)+B^(2) is always equal to

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