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Q. If A is a 3×3 nonsingular matrix and if |A|=3, then |(2A)1|= _______

KCETKCET 2010Determinants

Solution:

Given, |A|3×30 and |A|=3
Then, |(2A)1|=|12A|=1|2A|
=1(2)31|A|(|aA|=a3|A|)
=1813=124