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The inverse of the matrix open square brackets table row 3 cell negative 2 end cell row 1 4 end table close square bracketsis

  1. open square brackets table row cell fraction numerator 4 over denominator 14 end fraction end cell cell fraction numerator 2 over denominator 14 end fraction end cell row cell fraction numerator negative 1 over denominator 14 end fraction end cell cell fraction numerator 3 over denominator 14 end fraction end cell end table close square brackets    
  2. open square brackets table row cell fraction numerator 3 over denominator 14 end fraction end cell cell fraction numerator negative 2 over denominator 14 end fraction end cell row cell fraction numerator 1 over denominator 14 end fraction end cell cell fraction numerator 4 over denominator 14 end fraction end cell end table close square brackets    
  3. open square brackets table row cell fraction numerator 4 over denominator 14 end fraction end cell cell fraction numerator negative 2 over denominator 14 end fraction end cell row cell fraction numerator 1 over denominator 14 end fraction end cell cell fraction numerator 3 over denominator 14 end fraction end cell end table close square brackets    
  4. open square brackets table row cell fraction numerator 3 over denominator 14 end fraction end cell cell fraction numerator 2 over denominator 14 end fraction end cell row cell fraction numerator 1 over denominator 14 end fraction end cell cell fraction numerator 4 over denominator 14 end fraction end cell end table close square brackets    

The correct answer is: open square brackets table row cell fraction numerator 4 over denominator 14 end fraction end cell cell fraction numerator 2 over denominator 14 end fraction end cell row cell fraction numerator negative 1 over denominator 14 end fraction end cell cell fraction numerator 3 over denominator 14 end fraction end cell end table close square brackets


    Let A equals open square brackets table row 3 cell negative 2 end cell row 1 4 end table close square brackets rightwards double arrow vertical line A vertical line equals 14
    therefore a d j A equals open square brackets table row 4 2 row cell negative 1 end cell 3 end table close square brackets rightwards double arrow A to the power of negative 1 end exponent equals open square brackets table row cell fraction numerator 4 over denominator 14 end fraction end cell cell fraction numerator 2 over denominator 14 end fraction end cell row cell fraction numerator negative 1 over denominator 14 end fraction end cell cell fraction numerator 3 over denominator 14 end fraction end cell end table close square brackets.

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