I am interested in proving the following statement and would appreciate some guidance or help:
The set of all semi-magic squares is a subspace of the vector space of 3 x 3 matrices.
Where a matrix is said to be a semi-magic square if its row sums and column sums (i.e. the sum of entries in an individual row or column) all add up to the same number.
You only need to verify that $\lambda A$ and $A+B$ satisfy the given condition provided that $A$ and $B$ does and $\lambda\in\Bbb R$.