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Matrices

Question

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Give example to show that $AB space equals space straight O space even space if space straight A space not equal to space straight O comma space straight B space not equal to space straight O$

Solution

Let space straight A space equals space open square brackets table row 1 0 row 0 0 end table close square brackets space comma space space straight B equals space open square brackets table row 0 0 row 0 2 end table close square brackets therefore space 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 0 2 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 0 plus 0 end cell cell 0 plus 0 end cell end table close square brackets space equals space open square brackets table row 0 0 row 0 0 end table close square brackets equals 0 therefore space space space AB equals space space 0 space even space if space straight A space not equal to space 0 comma space straight B space not equal to space 0

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