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Let A be a non-singular matrix and B= adj A . Which of the following statements is/are correct? 1. A B=B A 2. A B is a scalar matrix 3. A B can be a null matrix Select the correct answer using the code given below :

Options

  1. A1 only
  2. B1 and 2 only
  3. C2 only
  4. D1, 2 and 3

Correct answer

B. 1 and 2 only

Step-by-step solution

Given that |A| 0 and B= adj AA B=A( adj A)=|A| I aligned & B A=[ adj (A)] A=|A| I & A B=B A aligned So, statement 1 is correct It is clear from (i) A B is a scalar matrix not null matrix So statement 2 is correct and 3 is not correct.

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