Consider the following in respect of matrices A, B and C of same order : 1. (A+B+C)'=A'+B'+C' 2. (AB)'=A'B' 3. (ABC)'=C'B'A' where A' is the transpose of the matrix A. Which of the above are correct?

NDA 2018 Mathematics question

Consider the following in respect of matrices A, B and C of same order : 1. 2. 3. where is the transpose of the matrix A. Which of the above are correct?

(A)1 and 2 only
(B)2 and 3 only
(C)1 and 3 onlyCorrect
(D)1, 2 and 3

Answer: (C)

Solution

The transpose of a sum is the sum of the transposes (1 correct). The transpose of a product reverses

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Question ID VK-028959