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AP EAMCET201822 Apr 2018Evening ShiftMathematicsMatricesActual

If A is a square matrix of order 3 , then consider the following statements. I. If |A|=0 , then | Adj A|=0 II. If |A| 0 , then |A⁻¹ |=|A|⁻¹ Which of the above statements is/are true?

Options

  1. ABoth I and II
  2. BNeither I nor II
  3. CI only
  4. DII only

Correct answer

A. Both I and II

Step-by-step solution

For a square matrix A of order 3 , | Adj A|=|A|³⁻¹=|A|^2 If |A|=0 , then | Adj A|=0 and A A⁻¹=I , if |A| 0 aligned & |A A⁻¹ |=|I| |A| |A⁻¹ |=1 & |A⁻¹ |=|A|⁻¹ & aligned So, statements I and II, both are correct.

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