What is the adjoint of an inverse matrix? Is $(T^{-1})^{*} = (T^{*})^{-1}$?
2026-03-28 19:30:55.1774726255
What is the adjoint of an inverse matrix?
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Since $TT^{-1}=I$, we can take adjoints to find $$(T^{-1})^*T^*=(TT^{-1})^*=I^*=I.$$ So $(T^{-1})^*$ is indeed the inverse of $T^*$.