Question

The eigen values of a \(3\times3\) real matrix \(A\) are \(1,-2,3\). Then

• A. \(A^{-1}=\dfrac{1}{6}(5I+2A-A^2)\)
• B. \(A^{-1}=\dfrac{1}{6}(5I-2A+A^2)\)
• C. \(A^{-1}=\dfrac{1}{6}(5I-2A-A^2)\)
• D. \(A^{-1}=\dfrac{1}{6}(5I+2A+A^2)\)

Hint:

For eigenvalue questions, \[ \boxed{ \text{Characteristic Polynomial} \rightarrow \text{Cayley--Hamilton} \rightarrow A^{-1} } \] Always multiply the Cayley--Hamilton equation by \(A^{-1}\) when inverse is required.

Answer 1

The Correct Option is A