prove or disprove invertible matrix with given equations Given a non-scalar matrix $A$ in size $n\times n$ over $\mathbb{R}$ that maintains the following equation 
$$A^2 + 2A = 3I$$
given matrix $B$ in size $n\times n$ too $$B = A^2 + A- 6I$$
Is $B$ an invertible matrix?

Hint: The first equation implies that $A^2+2A-3I=(A-I)(A+3I)=0$. Hence the minimal polynomial $m_A(x)$ of $A$ divides $(x-1)(x+3)$. What happens if $x+3$ is not a factor of $m_A(x)$?
