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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 \(\operatorname{Trace}(C)=\)

  1. A \(3\)
  2. B \(5\)
  3. C \(7\)
  4. D \(9\)
Verified Solution

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 &…