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[Solution Library] A matrix A ∈ M_n is a square root of B ∈ M_n if A^2=B . Show that every diagonalizable B ∈ M_n has a square root. Does B=[ll0

Question: A matrix \(A \in M_{n}\) is a square root of \(B \in M_{n}\) if \(A^{2}=B .\) Show that every diagonalizable \(B \in M_{n}\) has a square root. Does \(B=\left[\begin{array}{ll}0 & 1 \\ 0 & 0\end{array}\right]\) have a square root? Why?

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