AP EAMCET · Maths · Matrices
If \(A\) is a square matrix of order 3 and \(A^2+A+2 I=0\), then
- A A can not be a skew-symmetric matrix
- B \(|A+I|=0\)
- C \(A\) is non singular and \(A^{-1}=(A+I)^{-1}\)
- D \(|A||A+I|=2\)
Answer & Solution
Correct Answer
(A) A can not be a skew-symmetric matrix
Step-by-step Solution
Detailed explanation
Given matrix equation \(A^2+A+2 I=0\) \[ \Rightarrow \quad A(A+I)=-2 I \] \[ \begin{array}{lc} \Rightarrow & |A(A+I)|=|-2 I| \\ \Rightarrow & |A||A+I|=(-2)^3 \\ \Rightarrow & |A||(A+I)|=-8 \\ \Rightarrow & |A| \neq 0 \text { and }|A+I| \neq 0 \end{array} \] and the determinant…
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