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  • Solve it, If A and B are two matrices, such that AB = 0, then which of the following can be true ?

If A and B are two matrices, such that AB = 0, then which of the following can be true ?

  • Option 1)

    A = 0, B = 0

  • Option 2)

    A \neq 0, B = 0 or A = 0, B \neq 0

  • Option 3)

    A \neq 0, B \neq 0

  • Option 4)

    All of these

 

Answers (1)

best_answer

As we have learnt,

 

Property of matrix multiplication -

AB=0 does not necessarily imply that either A or B is a null matrix 

-

 

 Both matrices need not be null matrices.

 


Option 1)

A = 0, B = 0

Option 2)

A \neq 0, B = 0 or A = 0, B \neq 0

Option 3)

A \neq 0, B \neq 0

Option 4)

All of these

Posted by

gaurav

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