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If A and B are two matrices such that AB...

If A and B are two matrices such that `AB=B and BA=A` then `A^2+B^2=` (A) 2AB (B) 2BA (C) A+B (D) AB

A

`A^(2)+B^(2)`

B

`O`

C

`A^(2)+2AB+B^(2)`

D

`A+B`

Text Solution

AI Generated Solution

To solve the problem, we need to find the value of \( A^2 + B^2 \) given the conditions \( AB = B \) and \( BA = A \). ### Step-by-Step Solution: 1. **Start with the given equations**: We have: \[ AB = B \quad \text{(1)} ...
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Knowledge Check

  • If A and B are 3times3 matrices such that AB=A and BA=B, then

    A
    `A^(2)=A and B^(2)=B`
    B
    `A^(2)=A and B^(2)=!B`
    C
    `A^(2)=!A and B^(2)=B`
    D
    `A^(2)=!A and B^(2)=!B`

  • If A and B are two square matrices such that AB=A and BA=B , then A^(2) equals

    A
    B
    B
    A
    C
    `I`
    D
    O

  • Let A and B are two matrices such that AB = BA, then for every n in N

    A
    `A^(n) B = BA^(n)`
    B
    `(AB)^(n) = A^(n)B^(n)`
    C
    `(A+B)^(n) = ""^(n)C_(0) A^(n) + ""^(n)C_(1) A^(n-1) B+...+ ""^(n) C_(n) B^(n) `
    D
    `A^(2n) - B ^(2n) = (A^(n)-B^(n) ) (A^(n)+B^(n))`

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

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