Can the diagonalizing matrix be to the left of the matrix of interest?

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I've always diagonalized matrices in this way

$$S^{-1}AS = D$$

where $D$ diagonal and the columns of $S$ are the (linearly independent) eigenvectors of $A$.

Could I instead do $SAS^{-1}$? Is there an obvious flaw to this multiplication?

Thanks,

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The $S$ of one approach is the $S^{-1}$ of the other.