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    If λ ∈ R and A = (aij ) ∈ Mn(R), we say that A is λ-nice if
    the sum of the entries on any row of A is equal to λ and the sum of the entries on any
    column of A is equal to λ.
    For instance, the matrix
    1 2
    2 1
    is 3-nice.

    Let λ, µ ∈ R and A = (aij ), B = (bij ) ∈ Mn(R). Assume that A is λ-nice and B
    is µ-nice. Prove that A + B is (λ + µ)-nice. Is AB (λ · µ)-nice?#

    Can you help me please?
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    (Original post by doublemm)
    If λ ∈ R and A = (aij ) ∈ Mn(R), we say that A is λ-nice if
    the sum of the entries on any row of A is equal to λ and the sum of the entries on any
    column of A is equal to λ.
    For instance, the matrix
    1 2
    2 1
    is 3-nice.

    Let λ, µ ∈ R and A = (aij ), B = (bij ) ∈ Mn(R). Assume that A is λ-nice and B
    is µ-nice. Prove that A + B is (λ + µ)-nice. Is AB (λ µ)-nice?#

    Can you help me please?
    The answer to the sum part of this question is obvious; for the product, try and think of an example using stuff that's already been given to you in the question. What might you do with that 3-nice matric, for example?

    BTW, best to ask questions like this in the maths forum!
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    Would you use proof my induction?
 
 
 
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