I'm working through the problem and I start with $ABC = I = (AC)B = I... B = (AC)^{-1}$.. This is equal to $B = C^{-1} * A^{-1}$. However, I'm trying to show that $B = A^{-1} * C^{-1}$. Where am I going wrong? I feel as if I'm going in the right direction, but can't seem to tie it together.
2026-03-25 01:28:54.1774402134
Suppose that $A$ and $C$ are invertible matrices, and that $ABC = I$. Show $B = A^{−1}C^{ −1}$ .
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$ABC=I$
$A^{-1}ABC=A^{-1}I$
$BC=A^{-1}$
$BCC^{-1}=A^{-1}C^{-1}$
$B=A^{-1}C^{-1}$.