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Determinants

Question

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Find adj A for $straight A space equals space open square brackets table row 2 cell space space space 3 end cell row 1 cell space space space 4 end cell end table close square brackets.$

Solution

straight A space equals space open square brackets table row 2 cell space space space 3 end cell row 1 cell space space 4 end cell end table close square brackets straight A subscript 11 space equals space 4 comma space space space space straight A subscript 12 space equals space minus 1 comma space space straight A subscript 21 space equals space minus 3 comma space space straight A subscript 22 space equals space 2 therefore space space space space space adj space straight A space equals space open square brackets table row cell straight A subscript 11 end cell cell space space straight A subscript 12 end cell row cell straight A subscript 21 end cell cell space space straight A subscript 22 end cell end table close square brackets to the power of apostrophe space equals space open square brackets table row 4 cell negative 1 end cell row cell negative 3 end cell 2 end table close square brackets to the power of apostrophe space equals space open square brackets table row 4 cell space space space space minus 3 end cell row cell negative 1 end cell cell space space space space space space space space space 2 end cell end table close square brackets.

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