No you cannot, in general. But the extent to which you can, for a given matrix $A$, is quantified by the condition number $\kappa(A)$ of the matrix $A$, as the linked page explains competently.
For the sake of completeness, I append the answer I wrote for the other question (now closed as a duplicate) asked by the OP, whose formulation was:
Ill-conditioned matrix Consider this problem: $Ax=b$. I want to solve it/find $x$ and the matrix $A$ is ill-conditioned. Why is the fact that A is ill-conditioned a bad thing?
Because if one knows the coefficients of $A$ only up to a given precision, a small variation in them will cause a huge variation in the coefficients of $A^{-1}$, hence, presumably, in the solution $x=A^{-1}b$. Alternatively, even if $A^{-1}$ is known with an absolute precision, if one knows the coefficients of $b$ only up to a given precision, a small variation in them will cause a notable variation in the coefficients of the solution $x=A^{-1}b$ since some coefficients of $A^{-1}$ are large. In real life, both effects are often conspiring. See the definition of the condition number of a matrix.