I know that inverse of a matrix is given by $adj(A)/|A|$ but I cannot prove it.Nor did I find the proof in my books.Can you guide me?
2026-04-08 01:13:41.1775610821
Proof that $A^{-1}=adj(A)/|A|$
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If you calculate the product $A\cdot\text {adj}(A)$ (actually you need the transpose, but I assume you included it in your definition of adj), each entry is of the form "sum of elements of a row of $A $ times cofactors". For those elements not in the diagonal of $A $, these correspond to the determinant of a matrix with two repeated rows, so they are zero. The diagonal elements are precisely $|A|$.