Key facts If ∣A∣≠0|A|\ne 0∣A∣=0, then: A−1=1∣A∣adj(A)A^{-1}=\frac{1}{|A|}\operatorname{adj}(A)A−1=∣A∣1adj(A) and: AA−1=A−1A=IAA^{-1}=A^{-1}A=IAA−1=A−1A=I