AP EAMCET · Maths · Matrices
Let \(A=\left[\begin{array}{lll}n & 0 & 0 \\ 0 & n & 0 \\ 0 & 0 & n\end{array}\right]\) and \(B=\left[\begin{array}{lll}0 & 0 & n \\ 0 & n & 0 \\ n & 0 & 0\end{array}\right]\). Then, \(A^2+B^2+A B=\)
- A \(n(n l+n B+B)\)
- B \(n(2 n l+B)\)
- C \(n^2(2 l+B)\)
- D \(n(n l+n A+B)\)
Answer & Solution
Correct Answer
(B) \(n(2 n l+B)\)
Step-by-step Solution
Detailed explanation
\(A^2=\left[\begin{array}{ccc}n^2 & 0 & 0 \\ 0 & n^2 & 0 \\ 0 & 0 & n^2\end{array}\right], B^2=\left[\begin{array}{ccc}n^2 & 0 & 0 \\ 0 & n^2 & 0 \\ 0 & 0 & n^2\end{array}\right]\) \(A B=\left[\begin{array}{ccc}0 & 0 & n^2 \\ 0 & n^2 & 0 \\ n^2 & 0 & 0\end{array}\right]\) Now,…
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