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AP EAMCET · Maths · Matrices

If \(A\) and \(B\) are two matrices given by \(A=\left(\begin{array}{lll}1 & 2 & 3 \\ 2 & 3 & 4 \\ 5 & 6 & 8\end{array}\right)\) and \(B=\left(\begin{array}{lll}3 & 2 & 5 \\ 2 & 3 & 8 \\ 7 & 2 & 9\end{array}\right)\) then, the value of \(|\operatorname{Adj}(A B)|\) is

  1. A 24
  2. B \(24^2\)
  3. C \(24^3\)
  4. D 65
Verified Solution

Answer & Solution

Correct Answer

(B) \(24^2\)

Step-by-step Solution

Detailed explanation

\(|A| = 1(24-24) - 2(16-20) + 3(12-15) = 0 + 8 - 9 = -1\) \(|B| = 3(27-16) - 2(18-56) + 5(4-21) = 3(11) - 2(-38) + 5(-17) = 33 + 76 - 85 = 24\) \(| \operatorname{Adj}(AB) | = |AB|^{3-1} = (|A||B|)^2 = (-1 \cdot 24)^2 = (-24)^2 = 24^2\)