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AP EAMCET · Maths · Determinants

If \(A=\left[\begin{array}{cc}i & 0 \\ 0 & -i\end{array}\right], B=\left[\begin{array}{cc}0 & -1 \\ 1 & 0\end{array}\right]\) and \(C=\left[\begin{array}{ll}0 & i \\ i & 0\end{array}\right]\), then

  1. A \(\mathrm{A}^2+\mathrm{B}^2+\mathrm{C}^2=3 \mathrm{~A}^2 \mathrm{~B}^2 \mathrm{C}^2\)
  2. B \(\mathrm{A}^2+\mathrm{B}^2+\mathrm{C}^2=3 \mathrm{ABC}\)
  3. C \(\mathrm{A}^2+\mathrm{B}^2+\mathrm{C}^2=3 \mathrm{I}\)
  4. D \(\mathrm{A}^2+\mathrm{B}^2+\mathrm{C}^2=2 \mathrm{ABC}\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(\mathrm{A}^2+\mathrm{B}^2+\mathrm{C}^2=3 \mathrm{~A}^2 \mathrm{~B}^2 \mathrm{C}^2\)

Step-by-step Solution

Detailed explanation

\begin{aligned} & \text { } \mathrm{A}^2=\mathrm{A} \cdot \mathrm{A}=\left[\begin{array}{cc} -1 & 0 \\ 0 & -1 \end{array}\right], \mathrm{B}^2=\mathrm{B} \cdot \mathrm{B}=\left[\begin{array}{cc} -1 & 0 \\ 0 & -1 \end{array}\right] \\ & \mathrm{C}^2=\mathrm{C} \cdot…