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Matrices

Question
CBSEENMA12034288

If space straight A equals space open square brackets table row 1 2 3 row 3 cell negative 2 end cell 1 row 4 2 1 end table close square brackets space comma space then space straight A cubed space minus 23 space straight A space 40 space straight I space equals straight O

Solution
Here space space straight A equals space open square brackets table row 1 2 3 row 3 cell negative 2 end cell 1 row 4 2 1 end table close square brackets
therefore space space space space space space straight A to the power of italic 2 space equals open square brackets table row 1 2 3 row 3 cell negative 2 end cell 1 row 4 2 1 end table close square brackets space open square brackets table row 1 2 3 row 3 cell negative 2 end cell 1 row 4 2 1 end table close square brackets space
space space space space space space space space space space space space space space space space equals space space open square brackets table row cell 1 plus 6 minus 12 space space end cell cell space 2 minus 4 plus 6 end cell cell space space 3 plus 2 plus 3 end cell row cell 3 minus 6 plus 4 space end cell cell space 6 plus 4 plus 2 end cell cell space space 9 minus 2 plus 1 end cell row cell 4 plus 6 plus 4 end cell cell space 8 minus 4 plus 2 end cell cell space space 12 plus 2 plus 1 end cell end table close square brackets space equals open square brackets table row 19 4 8 row 1 12 8 row 14 6 15 end table close square brackets
space space space space space space space space space space space space straight A cubed space equals space space open square brackets table row 19 4 8 row 1 12 8 row 14 6 15 end table close square brackets space space open square brackets table row 1 2 3 row 3 cell negative 2 end cell 1 row 4 2 1 end table close square brackets
space space space space space space space space space space space space space space space space equals space space space open square brackets table row cell 19 plus 12 plus 32 end cell cell space space space 38 minus 8 plus 16 end cell cell space space space 57 plus 4 plus 8 end cell row cell 1 plus 36 plus 32 end cell cell space space space 2 minus 24 plus 16 end cell cell space space space 3 plus 12 plus 8 end cell row cell 14 plus 18 plus 60 end cell cell space space space 28 minus 12 plus 30 end cell cell space space space 42 plus 6 plus 15 end cell end table close square brackets equals space open square brackets table row 63 cell space space 46 end cell cell space space space 69 end cell row 69 cell space space space minus 6 end cell cell space space space 23 end cell row 92 cell space space 46 end cell cell space space space 63 end cell end table close square brackets
straight L. straight H. straight S space space minus straight A cubed space minus 23 straight A minus 40 space straight I
space space space space space space space space space space space space space space space space space equals space space open square brackets table row 63 cell space space space 46 end cell cell space space space 69 end cell row 69 cell space space minus 6 end cell cell space space space 23 end cell row cell 92 space space end cell cell space space 46 end cell cell space space space 63 end cell end table close square brackets minus 23 space open square brackets table row 1 cell space space 2 end cell cell space space 3 end cell row 3 cell space space minus 2 end cell cell space space 1 end cell row 4 cell space space 2 end cell cell space space 1 end cell end table close square brackets minus 40 space open square brackets table row 1 cell space space 0 end cell cell space space space 0 end cell row 0 cell space space 1 end cell cell space space space 0 end cell row 0 cell space space space space 0 end cell cell 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 equals space open square brackets table row 63 cell space space space 46 end cell cell space space space 69 end cell row 69 cell space space minus 6 end cell cell space space space 23 end cell row cell 92 space space end cell cell space space 46 end cell cell space space space 63 end cell end table close square brackets plus open square brackets table row cell negative 23 end cell cell space space space minus 46 end cell cell space space space minus 69 end cell row cell negative 69 end cell cell space space space space space space space space 46 end cell cell space space minus 23 end cell row cell negative 92 end cell cell space space minus 46 end cell cell space space space minus 23 end cell end table close square brackets plus space open square brackets table row cell negative 40 end cell 0 0 row 0 cell negative 40 end cell 0 row 0 0 cell negative 40 end cell end table close square brackets
space space space space space space space space space space space space space space space space equals space space space open square brackets table row cell 63 minus 23 minus 64 end cell cell space space space space space space 46 minus 46 plus 0 end cell cell space space space space space space space 69 minus 69 plus 0 end cell row cell 69 minus 69 plus 0 end cell cell negative 6 plus 46 minus 40 end cell cell space space space space space space space 23 minus 23 plus 0 end cell row cell 92 minus 92 plus 0 end cell cell space space space space space 46 minus 46 plus 0 end cell cell space space space space space space space space 63 minus 23 minus 40 end cell end table close square brackets space space space space equals open square brackets table row 0 cell space space space space 0 space space space space space end cell 0 row 0 0 0 row 0 0 0 end table close square brackets space space space equals straight O
straight R. straight H. straight S

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

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