TS EAMCET · Maths · Matrices
If \(\mathrm{A}\) is a non-singular matrix such that \((\mathrm{A}-2 \mathrm{I})(\mathrm{A}-3 \mathrm{I})=\mathrm{O}\), then \(\frac{1}{5} \mathrm{~A}+\frac{6}{5} \mathrm{~A}^{-1}=\)
- A \(\mathrm{O}\)
- B \(\mathrm{I}\)
- C \(\mathrm{2I}\)
- D \(\mathrm{3I}\)
Answer & Solution
Correct Answer
(B) \(\mathrm{I}\)
Step-by-step Solution
Detailed explanation
\[ \begin{aligned} & (A-2 I)(A-3 I)=0 \\ \Rightarrow & A^2-3 A-2 A+6 I^2=0 \Rightarrow A^2-5 A+6 I=0 \\ \Rightarrow & 6 I=5 A-A^2 \Rightarrow 6 I=A(5 I-A) \\ \Rightarrow & I=A\left(\frac{5 I-A}{6}\right) \\ \therefore & A^{-1}=\frac{5 I-A}{6} \end{aligned} \] Now,…
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