Matrices equal to sums (or operations) of rows and columns?

Question

If rows are i and columns are j so the order would be i x j. If A=(i+2j), B=(2i-j) where A and B are included in M_n. What would be the relationship between the matrices A+2B and -2A+B? That is the question the exercise asks, and the answer is obtained by plugging in the values of A and B into the matrices we want to compare (call them C and D respectively), so we get c_ij= 5i and d_ij= -5j And then we simplify and get c_ij = -d_ji (Notice that in d, _ij was swapped for _ji) So this means A+2B = -(-2A+B)^T.

I never saw an example like this before and don't understand how for instance A is expressed as a sum of rows and columns A=(i+2j). ¿Or might they mean i and j are variables with nothing to do with the rows and columns, but I don't think so?

¿How do they figure that a transpose needs to be applied?

I am just used to seeing matrices with numbers, variables or parameters but not as sums or operations with the rows and columns. And if M_n is supposed to be the set of all square matrices, i am not used to seeing something like A=(i+2j). I also noticed that they changed C and D from uppercase to lowercase, maybe they refer to an element within the matrix. I also thought that if A is a square matrix, then i should equal to j, but then in A=(i+2j), where does the + come in?

Thank you for your help!