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Tricks for solving IIT Mathematics

Basic ideas are highly useful for exams like IIT JAM & other M.Sc entrances.

Trick:- If A be an n×n non-singular matrix, then |adjA|=|A|^(n-1) .
Proof:- As we know that
        A.adjA = |A|.I
or,  det{ A.adjA }=det{ |A|.I }
or,  |A|.|adjA|= |A|ⁿ
Using   det(AB)=det(A).det(B)
and     det(|A|.I)=|A|ⁿ.I
Hence we get the result. [ As |A|≠0 ].

Problem: [IIT-JAM-2011(MA paper)] Let A be a 3×3 real matrix with det(A)=6. Then find det(adjA).
Sol:- Using the above result, putting n=3
So, det(adjA) = 6² =36.