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If the matrix AB is a zero matrix, then which one of the following is correct?

Options

  1. AA must be equal to zero matrix or B must be equal to zero matrix
  2. BA must be equal to zero matrix and B must be equal to zero matrix
  3. CIt is not necessary that either A is zero matrix or B is zero matrix
  4. DNone of the above

Correct answer

C. It is not necessary that either A is zero matrix or B is zero matrix

Step-by-step solution

If A= [ array ll 2 & 0 0 & 0 array ], B= [ array ll 0 & 0 2 & 0 array ] then, A B= [ array ll 0 & 0 0 & 0 array ] Here A 0, ~B 0 but AB =0 .

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