Question

$If space straight A equals open square brackets table row 1 cell negative 1 end cell 1 row 0 2 1 end table close square brackets comma space straight B space open square brackets table row 1 cell negative 1 end cell 0 row 0 1 cell negative 1 end cell row 1 1 1 end table close square brackets space comma straight C space open square brackets table row 1 0 row 0 1 row 1 1 end table close square brackets space verify space that space straight A space left parenthesis BC right parenthesis equals left parenthesis AB right parenthesis space straight C.$

Solution

straight A equals open square brackets table row 1 cell negative 1 end cell 1 row 0 2 1 end table close square brackets comma straight B equals open square brackets table row 1 cell negative 1 end cell 0 row 0 1 cell negative 1 end cell row 1 1 1 end table close square brackets comma space straight C equals open square brackets table row 1 0 row 0 1 row 1 1 end table close square brackets BC equals open square brackets table row 1 cell negative 1 end cell 0 row 0 1 cell negative 1 end cell row 1 1 1 end table close square brackets space open square brackets table row 1 0 row 0 1 row 1 1 end table close square brackets space equals space open square brackets table row cell 1 plus 0 plus 0 end cell cell 0 minus 1 plus 0 end cell row cell 0 plus 1 minus 1 end cell cell 0 plus 1 minus 1 end cell row cell 0 plus 1 plus 1 end cell cell 0 plus 1 plus 1 end cell end table close square brackets equals open square brackets table row 1 cell negative 1 end cell row cell negative 1 end cell 0 row 2 2 end table close square brackets space space space space space space space space space space space space space space space space space space space space space space space space AB equals open square brackets table row 1 cell negative 1 end cell 1 row 0 2 1 end table close square brackets space open square brackets table row 1 cell negative 1 end cell 0 row 0 1 cell negative 1 end cell row 1 1 1 end table close square brackets space space space space space space space space space space space space space space space space space space space space space space space space space space space equals open square brackets table row cell 1 plus 0 plus 1 end cell cell negative 1 minus 1 plus 1 end cell cell 0 plus 1 plus 1 end cell row cell 0 plus 0 plus 1 end cell cell 0 plus 2 plus 1 end cell cell 0 minus 2 plus 1 end cell end table close square brackets equals open square brackets table row 2 cell negative 1 end cell 2 row 1 3 cell negative 1 end cell end table close square brackets space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space straight L. straight H. straight S space equals space straight A left parenthesis BC right parenthesis equals open square brackets table row 1 cell negative 1 end cell 1 row 0 2 1 end table close square brackets space space space open square brackets table row 1 cell negative 1 end cell row cell negative 1 end cell 0 row 2 2 end table close square brackets space space space space space space space space space space space space space space space space space straight R. straight H. straight S space equals space left parenthesis AB right parenthesis straight C space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space open square brackets table row 2 cell negative 1 end cell 2 row 1 3 cell negative 1 end cell end table close square brackets space space space space space space space open square brackets table row 1 0 row 0 1 row 1 1 end table close square brackets space space equals open square brackets table row cell 2 plus 0 plus 2 end cell cell 0 minus 1 plus 2 end cell row cell 1 plus 0 minus 1 end cell cell 0 plus 3 minus 1 end cell end table close square brackets space equals open square brackets table row 4 1 row 0 2 end table close square brackets therefore space space space space space space space space straight L. straight H. straight S space equals space space space space straight R. straight H. straight S space space space space space therefore space space space space space space space space space straight A left parenthesis BC right parenthesis space equals space left parenthesis AB right parenthesis straight C space is space verified. space space space space space

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