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Determinants

Question
CBSEENMA12034576
Wired Faculty App

If straight A space equals space open square brackets table row 2 cell space space space 7 end cell row 1 cell space space space 4 end cell end table close square brackets comma space space show that straight A squared minus 6 straight A space plus space straight I space equals space straight O comma space hence space find space straight A to the power of negative 1 end exponent.

Solution
straight A space equals open square brackets table row 2 cell space space space space 7 end cell row 1 cell space space space 4 end cell end table close square brackets
therefore space space space straight A squared space equals space open square brackets table row 2 cell space space space space 7 end cell row 1 cell space space space 4 end cell end table close square brackets space open square brackets table row 2 cell space space space 7 end cell row 1 cell space space space 4 end cell end table close square brackets space equals space open square brackets table row cell 4 plus 7 end cell cell space space space 14 plus 28 end cell row cell 2 plus 4 end cell cell space space 7 plus 16 end cell end table close square brackets space equals space open square brackets table row 11 cell space space 42 end cell row 6 cell space space 23 end cell end table close square brackets therefore space space space space straight A squared minus 6 straight A plus straight I space equals open square brackets table row 11 cell space space space space 42 end cell row 6 cell space space 23 end cell end table close square brackets space minus space open square brackets table row 2 cell space space space space 7 end cell row 1 cell space space space 4 end cell end table close square brackets space plus space open square brackets table row 1 cell space space space 0 end cell row 0 cell space space space 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 equals space open square brackets table row 11 cell space space 42 end cell row 6 cell space 23 end cell end table close square brackets space plus space open square brackets table row cell negative 12 end cell cell space space space minus 42 end cell row cell negative 6 end cell cell space space minus 24 end cell end table close square brackets space plus space open square brackets table row 1 cell space space space 0 end cell row 0 cell space space space 1 end cell end table close square brackets
                         equals space open square brackets table row cell 11 minus 12 plus 1 end cell cell space space space 42 minus 42 plus 0 end cell row cell 6 minus 6 plus 0 end cell cell space space space 23 minus 24 plus 1 end cell end table close square brackets space equals space open square brackets table row 0 cell space space 0 end cell row 0 cell space space 0 end cell end table close square brackets

therefore space space space space space straight A squared minus 6 straight A plus straight I space equals space straight O space space space space space space space space space space space space space space space space space space space space space space space space rightwards double arrow space space space straight I space equals space minus straight A squared plus 6 straight A rightwards double arrow space space space space space straight I thin space straight A to the power of negative 1 end exponent space equals space minus straight A squared straight A to the power of negative 1 end exponent space plus space 6 AA to the power of negative 1 end exponent space space space space space space rightwards double arrow space space straight A to the power of negative 1 end exponent space equals space minus straight A space plus space 6 thin space straight I therefore space space space space space space space straight A to the power of negative 1 end exponent space equals space minus open square brackets table row 2 cell space space space 7 end cell row 1 cell space space 4 end cell end table close square brackets plus 6 space open square brackets table row 1 cell space space space 0 end cell row 0 cell space space space 1 end cell end table close square brackets space equals space open square brackets table row cell negative 2 end cell cell space space space minus 7 end cell row cell negative 1 end cell cell space space minus 4 end cell end table close square brackets space plus space open square brackets table row 6 cell space space 0 end cell row 0 cell space space 6 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 equals space open square brackets table row cell negative 2 plus 6 end cell cell space space space space space space minus 7 plus 0 end cell row cell negative 1 plus 0 end cell cell space space space space space minus 4 plus 6 end cell end table close square brackets space equals space open square brackets table row cell space space 4 end cell cell space space space minus 7 end cell row cell negative 1 end cell cell space space space space space 2 end cell end table close square brackets

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