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# Matrices watch

1. 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?
2. (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!
3. Would you use proof my induction?

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