- #1

evinda

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MHB

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If the matrix $A \in M_n(\mathbb{C})$ has $m_A(x)=(x^2+1)(x^2-1)$ as its minimal polynomial, then I want to find the minimal polynomials of the matrices $A^2$ and $A^3$.

($M_n(k)$=the $n \times n$ matrices with elements over the field $k=\mathbb{R}$ or $k=\mathbb{C}$)

Is there a relation that connects the minimal polynomial of a matrix $B$ with the minimal polynomial of the powers of $B$ ? (Thinking)