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AP EAMCET · Maths · Determinants

If \(A=\left[\begin{array}{lll}1 & 0 & 2 \\ 2 & 1 & 3 \\ 3 & 2 & 4\end{array}\right]\), then \(A^2-5 A+6 I=\)

  1. A \(\left[\begin{array}{ccc}8 & 4 & 0 \\ 3 & 8 & 4 \\ 4 & 0 & 12\end{array}\right]\)
  2. B \(\left[\begin{array}{ccc}8 & 4 & 0 \\ 3 & 6 & 4 \\ 4 & 0 & 14\end{array}\right]\)
  3. C \(\left[\begin{array}{ccc}8 & 6 & 0 \\ 3 & 8 & 4 \\ 2 & 0 & 14\end{array}\right]\)
  4. D \(\left[\begin{array}{ccc}8 & 4 & 0 \\ 3 & 8 & 4 \\ 4 & 0 & 14\end{array}\right]\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(\left[\begin{array}{ccc}8 & 4 & 0 \\ 3 & 8 & 4 \\ 4 & 0 & 14\end{array}\right]\)

Step-by-step Solution

Detailed explanation

\(A=\left[\begin{array}{lll}1 & 0 & 2 \\ 2 & 1 & 3 \\ 3 & 2 & 4\end{array}\right] A^2=\left[\begin{array}{ccc}7 & 4 & 10 \\ 13 & 7 & 19 \\ 19 & 10 & 28\end{array}\right]\)…