Solution
= Solution
Since $A^2+I=0$, its <minimal polynomial> $m_A$ divides $X^2+1$. The <polynomial> $X^2+1$ is an <irreducible polynomial> over the <rational numbers>: a reducible quadratic would have a rational root, whereas $r^2+1>0$ for every $r\in\mathbb Q$.
Because $n>0$, the constant <polynomial> one evaluates to the nonzero <identity matrix> $I$, so $m_A\ne1$. Both $m_A$ and $X^2+1$ are <monic polynomials>; hence the only remaining divisor is
$$
\boxed{m_A(X)=X^2+1}.
$$