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AP EAMCET · Maths · Matrices

Let \(M=\left[\begin{array}{lll}1 & 2 & 2 \\ 2 & 1 & 2 \\ 2 & 2 & 1\end{array}\right]\) and \(I\) be the identity matrix of order 3 . Then \(M^2-4 M=\)

  1. A \(5 I\)
  2. B \(3 I\)
  3. C \(2 I\)
  4. D \(I\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(5 I\)

Step-by-step Solution

Detailed explanation

\(M = \left[\begin{array}{lll}1 & 2 & 2 \\ 2 & 1 & 2 \\ 2 & 2 & 1\end{array}\right] = 2\left[\begin{array}{lll}1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1\end{array}\right] - \left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{array}\right] = 2J - I\) \(J^2 = 3J\)…