What is the dimension of the space of all $n \times n$ matrices with real entries which are such that the sum of the entries in the first row and the sum of the diagonal entries are both zero?
I tried by finding number of independent entries. The number of independent entries on the diagonal is $n-1$. The number of upper triangular independent entries is $\frac{n(n-1)}{2}-1(n-1)$, and the number of lowertriangular independent entries is $\frac{n(n-1)}{2}$. Now adding them will give dimension. Am I right?