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Consider the following statements in respect of a non-singular matrix A of order n : 1. A ( adj A ^ T )= A ( adj A )^ T 2. If A ^2= A , then A is identity matrix of order n 3. If A ^3= A , then A is identity matrix of order n Which of the statements given above are correct?

Options

  1. A1 and 2 only
  2. B2 and 3 only
  3. C1 and 3 only
  4. D1, 2 and 3

Correct answer

D. 1, 2 and 3

Step-by-step solution

Statement 1 is correct. We have if A ^n= A then A is identity matrix Statements 2 and 3 are correct. Hence, all statement are correct.

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