Let $A \in \mathbb{R}^{N \times N}$ be a D6160: Real square matrix.
A D6160: Real square matrix $B \in \mathbb{R}^{N \times N}$ is a square root for $A$ if and only if
\begin{equation}
A = B^2
\end{equation}
Let $A \in \mathbb{R}^{N \times N}$ be a D6160: Real square matrix.
A D6160: Real square matrix $B \in \mathbb{R}^{N \times N}$ is a square root for $A$ if and only if
\begin{equation}
A = B B
\end{equation}