MHT CET · Maths · Matrices
If \(\mathrm{A}=\left[\begin{array}{cc}2 & 3 \\ 5 & -2\end{array}\right]\) and \(\mathrm{A}^{-1}=\mathrm{KA}\), then \(\mathrm{K}\) is
- A 19
- B \(\frac{-1}{19}\)
- C \(-19\)
- D \(\frac{1}{19}\)
Answer & Solution
Correct Answer
(D) \(\frac{1}{19}\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & A=\left[\begin{array}{cc}2 & 3 \\ 5 & -2\end{array}\right] \\ & |A|-4-15=-19 \text { and adj } A=\left[\begin{array}{cc}-2 & -3 \\ -5 & 2\end{array}\right] \\ & \therefore A^{-1}=\frac{-1}{19}\left[\begin{array}{cc}-2 & -3 \\ -5 & 2\end{array}\right]=\frac{1}{19}\left[\begin{array}{cc}2 & 3 \\ 5 & -2\end{array}\right] \Rightarrow \mathrm{k}=\frac{1}{19}\end{aligned}\)
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