AP EAMCET · Maths · Matrices
If a matrix \(A\) satisfies the equation \(A^3-6 A^2+11 A-6 I=0\), then \(A^{-1}\) can be
- A \(\frac{1}{4}\)
- B \(41\)
- C \(31\)
- D \(\frac{1}{3} /\)
Answer & Solution
Correct Answer
(D) \(\frac{1}{3} /\)
Step-by-step Solution
Detailed explanation
\[ \begin{aligned} & A^3-6 A^2+11 A-6 I=0 \\ & A^3-A^2-5 A^2+5 A+6 A-6 I=0 \\ & \Rightarrow A^2[A-I]-5 A[A-I]+6[A-I]=0 \\ & \Rightarrow {[A-I]\left[A^2-5 A+6\right]=0 } \\ & \Rightarrow(A-I)(A-2 I)(A-3 I)=0 \end{aligned} \] \(\therefore A-3 I\) can be a zero matrix.…
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