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Matrices

Question

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

Solution

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

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