AP EAMCET · Maths · Matrices
If \(A=\left[\begin{array}{cc}0 & -1 \\ 1 & 0\end{array}\right]\), then the incorrect option among the following is
- A \(A^3-I=A(A-I)\)
- B \(\left(A^3+I\right)=A\left(A^3-I\right)\)
- C \(A^4-I=A^2+I\)
- D \(A^2+I=A\left(A^2-l\right)\)
Answer & Solution
Correct Answer
(D) \(A^2+I=A\left(A^2-l\right)\)
Step-by-step Solution
Detailed explanation
For the given matrix \(A=\left[\begin{array}{cc}0 & -1 \\ 1 & 0\end{array}\right]\) the characteristics equation is \(A^2+I=0\), so the \(A^3=-A\) and \(A^4=I\). Now, if we analyse, the option \(A^2+I=A\left(A^2-I\right)\) is incorrect.
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