Let $X = A + iB \in \Bbb C^{n \times n}$ be nonsingular, where $A$ and $B$ are real $n \times n$ matrices. Show that $X^{-1}$ can be expressed in terms of the inverse of the real matrix of order $2n$ $$ Y = \begin{pmatrix} A & -B \\ B & A \\ \end{pmatrix}. $$ Compare the economics of real versus complex matrix inversion.
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