GO Classes | DA Course | Linear Algebra

Let $A$ be an $n \times n$ invertible matrix with real entries whose row sums are all equal to $c$. Consider the following statements:

1. Every row in the matrix $2 A$ sums to $2 c$.
2. Every row in the matrix $A^2$ sums to $c^2$.
3. Every row in the matrix $A^{-1}$ sums to $c^{-1}$.

Which of the following is TRUE?

1. None of the statements (1), (2), (3) is correct.
2. Statement (1) is correct but not necessarily statements (2) or (3).
3. Statement (2) is correct but not necessarily statements (1) or (3).
4. All the three statements (1), (2), and (3) are correct.