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Consider the following statements in respect of square matrices A, B, C each of same order n : 1. A B=A C B=C if A is non-singular 2. If B X=C X for every column matrix X having n rows then B=C Which of the statement given above is/are correct?

Options

  1. A1 only
  2. B2 only
  3. CBoth 1 and 2
  4. DNeither 1 nor 2

Correct answer

A. 1 only

Step-by-step solution

A B=A C If A is non singular hence A⁻¹ exist. A⁻¹ A B=A⁻¹ A C B=C but B X=C X B=C is not necessarily true. e.g. [ array ll 1 & 2 3 & 4 array ] [ array l 0 0 array ]= [ array ll 2 & 3 7 & 5 array ] [ array l 0 0 array ] .

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