Welcome to Ctanujit Institute of Statistics & Mathematics...An Initiative by 'ISI'ian

Urgent Notice:

Due to unavoidable reason, Ctanujit Classes will be closed from 1st November to 30th November 2018.
Postal Package will be available from 1st December 2018.

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.