Let $M_{n \times n}$ be the set of all $n$-square matrices and the characteristics polynomial of each $A\in M_{n \times n}$ is of the form $a_nt^n+a_{n-1}t^{n-1}+...+a_1t+a_0$. Then the dimension of $M_{n \times n}$ over $\mathbb{R}$ is...
The answer provided is $(n-1)(n+2)/2$. I don't have any idea about how to approach it.
All I know, that in general, $\dim(M_{n \times n})=n^2$ and every square matrix satisfies its characteristic polynomial. Please help me out.