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Question:

If for any 2x2 square matrix A, A(adjA) = [8 0; 0 8], then write the value of det[A].

Solution:

let A =[a b; c d]
Adj(A) =[d -b; -c a]
Now A(AdjA)=[a b; c d] * [d -b; -c a] => [8 0; 0 8]=[a b; c d] * [d -b; -c a] => ad-bc=8, -ab+ab=0, dc-dc=0, -bc+ad=8
det(A)=|a b; c d|=ad-bc=8