AP EAMCET · Maths · Matrices
Let \(X=\left[\begin{array}{cc}1 & -1 \\ 1 & 1\end{array}\right]\), Let \(Y\) be a \(2 \times 2\) real matrix satisfying the condition \(X Y=Y X\). Then the smallest possible value of \(\operatorname{det}(Y)\) is
- A \(0\)
- B \(-2\)
- C \(-1\)
- D \(\frac{1}{2}\)
Answer & Solution
Correct Answer
(A) \(0\)
Step-by-step Solution
Detailed explanation
\(X=\left[\begin{array}{cc}1 & -1 \\ 1 & 1\end{array}\right], Y_{2 \times 2}=?, X Y=Y X\) Let \(Y=\left[\begin{array}{ll}x & y \\ z & t\end{array}\right]\) such that \(X Y=Y Z\)…
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