Question

Standard results ( rightarrow )
(1) ( A cdot operatorname{adj} A=|A| operatorname{In} )
(2) det ( (a d j A)=|A|^{n-1} )
(3) ( operatorname{det}(operatorname{adj}(a d j A))=|A|^{n^{2}-2 n+1}=|A| )
Heref ( =4) ) ( operatorname{det}(A)=|A|=begin{array}{c}text { product of diagonal elements } (text { since Ais a diagonal matix })end{array} )

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Solution