TS EAMCET · Maths · Matrices
\(A=\left[\begin{array}{ll}1 & 2 \\ 2 & 1\end{array}\right]\) and \(B=\left[\begin{array}{ll}x & y \\ 1 & 2\end{array}\right]\) are two matrices such that \((A+B)(A-B)=A^2-B^2\). If \(C=\left[\begin{array}{ll}x & 2 \\ 1 & y\end{array}\right]\) then \(\operatorname{Trace}(C)=\)
- A \(3\)
- B \(5\)
- C \(7\)
- D \(9\)
Answer & Solution
Correct Answer
(A) \(3\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { }(A+B)(A-B)=A^2-B^2 \\ & A^2-A B+B A-B^2=A^2-B^2 \Rightarrow A B=B A \\ & \Rightarrow\left[\begin{array}{ll}1 & 2 \\ 2 & 1\end{array}\right]\left[\begin{array}{ll}x & y \\ 1 & 2\end{array}\right]=\left[\begin{array}{ll}x & y \\ 1 &…
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