JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
If \(A\, = \,\left[ {\begin{array}{*{20}{c}}
0&{ - 1}\\
1&0
\end{array}} \right],\) then which one of the following statements is not correct?
- A \(A^2 + I = A(A^2 - I)\)
- B \(A^4 - I = A^2 + I\)
- C \(A^3 + I = A(A^3 - I)\)
- D \(A^3 - I = A(A- I)\)
Answer & Solution
Correct Answer
(A) \(A^2 + I = A(A^2 - I)\)
Step-by-step Solution
Detailed explanation
Given that \(A = \left[ {\begin{array}{*{20}{c}} 0&{ - 1}\\ 1&0 \end{array}} \right]\) \({A^2} = \left[ {\begin{array}{*{20}{c}} { - 1}&0\\ 0&{ - 1} \end{array}} \right] \Rightarrow {A^2} = - I\) \({A^3} = \left[ {\begin{array}{*{20}{c}} 0&1\\ { - 1}&0 \end{array}} \right]\)…
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