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GUJCET · Maths · Matrices
If \(A=\left[\begin{array}{lll}1 & 4 & 4 \\ 4 & 1 & 4 \\ 4 & 4 & 1\end{array}\right]\) then, \(A^2-6 A=\) ____________
- A \(27 I _3\)
- B \(5 I _3\)
- C \(20 I _3\)
- D \(30 I _3\)
Answer & Solution
Correct Answer
(A) \(27 I _3\)
Step-by-step Solution
Detailed explanation
\(A^2 = \left[\begin{array}{lll}1 & 4 & 4 \\ 4 & 1 & 4 \\ 4 & 4 & 1\end{array}\right] \left[\begin{array}{lll}1 & 4 & 4 \\ 4 & 1 & 4 \\ 4 & 4 & 1\end{array}\right] = \left[\begin{array}{lll}1+16+16 & 4+4+16 & 4+16+4 \\ 4+4+16 & 16+1+16 & 16+4+4 \\ 4+16+4 & 16+4+4 & 16+16+1\end{array}\right] = \left[\begin{array}{lll}33 & 24 & 24 \\ 24 & 33 & 24 \\ 24 & 24 & 33\end{array}\right]\) \(6A = 6 \left[\begin{array}{lll}1 & 4 & 4 \\ 4 & 1 & 4 \\ 4 & 4 & 1\end{array}\right] = \left[\begin{array}{lll}6 & 24 & 24 \\ 24 & 6 & 24 \\ 24 & 24 & 6\end{array}\right]\)
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