TS EAMCET · Maths · Matrices
If \(A, B\) are two non singular matrices of order \(3,|B|=k\), a positive integer, then match the items of list-I with the items of list-II.
The correct match is
\(\begin{array}{llll}
A & B & C & D
\end{array}\)
- A \(\begin{array}{llll}\text { III } & \mathrm{V} & \text{II} & \text { IV }\end{array}\)
- B \(\begin{array}{llll}\text { III } & \mathrm{IV} & \text{I} & \text { II }\end{array}\)
- C \(\begin{array}{llll}\text { I } & \mathrm{V} & \text{II} & \text { IV }\end{array}\)
- D \(\begin{array}{llll}\text { III } & \mathrm{IV} & \text{II} & \text { I }\end{array}\)
Answer & Solution
Correct Answer
(A) \(\begin{array}{llll}\text { III } & \mathrm{V} & \text{II} & \text { IV }\end{array}\)
Step-by-step Solution
Detailed explanation
It is given that the matrices \(A\) and \(B\) are non-singular of order 3 and \(|B|=k\), \(a\) positive integer, so \(\left|k^{-1} A^{-1}\right| =\left(k^{-1}\right)^3\left|A^{-1}\right|=\frac{1}{k^3|A|} \left[\because\left|A^{-1}\right|=\frac{1}{|A|}\right] \)…
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