Final answer:
Having equal row sums in an nxn matrix does not give enough information to conclude that the matrix is invertible, diagonal, symmetric, or a scalar matrix. The property only tells us about the uniformity of the sum of the elements in each row, not the matrix's detailed structure or features.
Step-by-step explanation:
If we consider an nxn matrix A with the property that the row sums are all equal, we cannot conclude that A is invertible, a diagonal matrix, symmetric, nor a scalar matrix solely based on this property. The information given suggests a uniform distribution of elements in terms of their sum per row, but this does not impose any specific structure regarding the invertibility, symmetry, diagonal form, or scalar nature of the matrix.
For example, a matrix having ones in all entries will have equal row sums but is not invertible for n > 1. Conversely, a diagonal matrix with nonzero values on the diagonal and zeros elsewhere might have equal row sums if all diagonal elements are equal, but this is not a requirement of a diagonal matrix in general.