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Let A be a matrix of order 3 × 3 such that det( A ) = 2, B = 2 A –1 and C = ( a d j A ) 16 3 , then the value of det( A 3 B 2 C 3 ) is

Correct answer

2

Step-by-step solution

A = 2 ,   B = 2 A - 1 = 2 3 | A | = 2 2 C = a d j A 16 3 = 1 16 ⋅ 2 2 = 1 2 2 ∴ d e t . A 3 B 2 C 3 = 2 3 ⋅ 2 2 2 ⋅ 1 2 2 3 = 2

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