### Group inverse for the block matrix with two identical subblocks over skew fields.

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The sign pattern of a real matrix $A$, denoted by $\mathrm{sgn}A$, is the $(+,-,0)$-matrix obtained from $A$ by replacing each entry by its sign. Let $\mathcal{Q}\left(A\right)$ denote the set of all real matrices $B$ such that $\mathrm{sgn}B=\mathrm{sgn}A$. For a square real matrix $A$, the Drazin inverse of $A$ is the unique real matrix $X$ such that ${A}^{k+1}X={A}^{k}$, $XAX=X$ and $AX=XA$, where $k$ is the Drazin index of $A$. We say that $A$ has signed Drazin inverse if $\mathrm{sgn}{\tilde{A}}^{\mathrm{d}}=\mathrm{sgn}{A}^{\mathrm{d}}$ for any $\tilde{A}\in \mathcal{Q}\left(A\right)$, where ${A}^{\mathrm{d}}$ denotes the Drazin inverse of $A$. In this paper, we give necessary conditions for some block triangular matrices to have signed...

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