TS EAMCET · Maths · Matrices
If \(A\) is a non-zero square matrix of order \(n\) with \(\operatorname{det}(I+A) \neq 0\) and \(A^3=O\), where \(I, O\) are unit and null matrices of order \(n \times n\) respectively, then \((I+A)^{-1}\) is equal to
- A \(I-A+A^2\)
- B \(I+A+A^2\)
- C \(I+A^{-1}\)
- D \(I+A\)
Answer & Solution
Correct Answer
(A) \(I-A+A^2\)
Step-by-step Solution
Detailed explanation
Given, \(|I+A| \neq O\) ie, \((A+I)\) is a non-singular matrix. \(O \rightarrow\) Null Matrix \(I \rightarrow\) Unit Matrix \(\because \quad I^3=I\) \(\Rightarrow \quad A^3=0\) \(\Rightarrow \quad A^3+I=O+I\) \(\Rightarrow \quad A^3+I^3=O+I\)…
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