Consider the following statements in respect of two non-singular matrices A and B of the same order n : 1. adj(AB)=(adjA)(adjB) 2. adj(AB)=adj(BA) 3. (AB)adj(AB)-|AB|I_n is a null matrix of order n How many of the above statements are correct?

NDA 2024 Mathematics question

Consider the following statements in respect of two non-singular matrices and of the same order : 1. adj(AB)=(adjA)(adjB) 2. adj(AB)=adj(BA) 3. (AB)adj(AB)-|AB|I_n is a null matrix of order How many of the above statements are correct?

(A)None
(B)Only one statementCorrect
(C)Only two statements
(D)All three statements

Answer: (B)

Solution

1: the correct rule is adj(AB) = (adjB)(adjA); the order is reversed, so statement 1 is not true in general. 2: in general, so $adj(AB)≠

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Question ID VK-029782