For a square matrix A, which of the following properties hold? 1. ({A}^{-1})^{-1}={A} 2. {\det}(A^{-1})= \frac{1}{{\det}A} 3. (\lambdaA)^{-1}\lambdaA^{-1} where λ is a scalar Select the correct answer using the code given below: [NDA II 2018]

Correct Answer is : 1 and 2 only

UPSC NDA II 2018 Mathematics Solved Paper

Question : 12 of 120

Marks: +1, -0

For a square matrix A, which of the following properties hold?
1. (A−1)−1=A
2. det(A−1)=‌‌

det‌A

3. (λA)−1λA−1 where λ is a scalar
Select the correct answer using the code given below:

[NDA II 2018]

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