Give example to show that AB ≠ O but BA = O.

Solution

Let space straight A equals space open square brackets table row 0 0 row 3 0 end table close square brackets space space space space space straight B equals space open square brackets table row 1 0 row 0 0 end table close square brackets therefore space AB equals space open square brackets table row 0 0 row 3 0 end table close square brackets space space open square brackets table row 1 0 row 0 0 end table close square brackets space equals space open square brackets table row cell 0 plus 0 end cell cell 0 plus 0 end cell row cell 3 plus 0 end cell cell 0 plus 0 end cell end table close square brackets equals open square brackets table row 0 0 row 3 0 end table close square brackets space not equal to 0 space space space space space BA equals space space open square brackets table row 1 0 row 0 0 end table close square brackets space open square brackets table row 0 0 row 3 0 end table close square brackets space space equals open square brackets table row cell 0 plus 0 end cell cell 0 plus 0 end cell row cell 0 plus 0 end cell cell 0 plus 0 end cell end table close square brackets equals open square brackets table row 0 0 row 0 0 end table close square brackets equals 0 therefore space AB space not equal to space straight O space comma space but space BA equals straight O

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