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AP EAMCET · Maths · Matrices

If \(A=\left[\begin{array}{ccc}1 & -3 & 2 \\ -2 & 1 & 3 \\ 3 & 2 & -1\end{array}\right]\) then \(A^2 \operatorname{Adj} A=\)

  1. A \(21 \mathrm{~A}\)
  2. B \(-42 \mathrm{~A}\)
  3. C \(7 \mathrm{~A}-1\)
  4. D \(14(\operatorname{Adj} A)\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(-42 \mathrm{~A}\)

Step-by-step Solution

Detailed explanation

\(|\mathrm{A}|\left|\begin{array}{ccc}1 & -3 & 2 \\ -2 & 1 & 3 \\ 3 & 2 & -1\end{array}\right|\) \(\begin{aligned} & =1-(-1-6)+3(2-9)+2(-4-3) \\ & =-7-21-14=-42\end{aligned}\) Now, \(A^2 \operatorname{adj} A=A \cdot A \operatorname{adj} A=A|A|=-42\)