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Consider the following statements in respect of two non-singular matrices A and B of the same order n : 1. adj ( AB )=( adj A )( 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?

Options

  1. ANone
  2. BOnly one statement
  3. COnly two statements
  4. DAll three statements

Correct answer

B. Only one statement

Step-by-step solution

Statements: 1. adj ( AB )=( adj A )( adjB ) Statement 1 is not correct. 2. AB BA adj ( AB ) adj ( BA ) Statement 2 is not correct. 3. aligned & ( AB ) adj ( AB )-| AB | I _n aligned aligned | AB | I _n-| AB | I _n aligned [ Aadj A =| A | I ]= Null matrix Hence, statement 3 is correct.

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