say I want to solve for $Y$
$$(Y+BC^T)^{-1} = A$$
taking inverse of both sides and then solving it for $Y$ yields to :
$$Y = A^{-1} - BC^{T}$$
2026-04-14 15:04:56.1776179096
is it valid to take an inverse of boths sides of a matrix equation?
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Yes, those operations are valid.
We can apply the same operations on both sides of an equality.