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Let A and B be square matrices of the...

Let `A` and `B` be square matrices of the same order. Does `(A+B)^2=A^2+2A B+B^2` hold? If not, why?

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If A and B are square matrices of the same order then (A+B)^2=A^2+2AB+B^2 implies

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Knowledge Check

  • If A and B are square matrices of same order, then (A+B) (A-B) is equal to

    A
    `A^(2)B^(2)`
    B
    `A^(2)=BA-AB+B^(2)`
    C
    `A^(2)-AB+BA-B^(2)`
    D
    `A^(2)+AB-BA-B^(2)`

  • If A and B arę square matrices of same order such that AB = A and BA = B, then

    A
    `A^(2)=A,B^(2)=B`
    B
    `A^(2)=A,B^(2) neB`
    C
    `B^(2)=B,A^(2) neA`
    D
    `A^(2) ne A,B^(2) neB`

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    If A and B are any two square matrices of the same order than ,

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