Maths-
General
Easy

Question

The inverse of matrix A equals open square brackets table row 0 1 0 row 1 0 0 row 0 0 1 end table close square bracketsis

  1. A    
  2. A to the power of T end exponent    
  3. open square brackets table row 1 0 0 row 0 1 0 row 0 0 1 end table close square brackets    
  4. open square brackets table row 1 0 0 row 1 0 0 row 0 1 0 end table close square brackets    

The correct answer is: A


    A equals open square brackets table row 0 1 0 row 1 0 0 row 0 0 1 end table close square brackets rightwards double arrow vertical line A vertical line equals negative 1 left parenthesis 1 plus 0 right parenthesis equals negative 1
    a d j left parenthesis A right parenthesis equals open square brackets table row cell A subscript 11 end subscript end cell cell A subscript 21 end subscript end cell cell A subscript 31 end subscript end cell row cell A subscript 12 end subscript end cell cell A subscript 22 end subscript end cell cell A subscript 32 end subscript end cell row cell A subscript 13 end subscript end cell cell A subscript 23 end subscript end cell cell A subscript 33 end subscript end cell end table close square brackets
    fraction numerator left parenthesis negative 1 right parenthesis to the power of 3 plus 2 end exponent M subscript 32 end subscript over denominator negative 2 end fraction comma text end text equals fraction numerator negative left parenthesis negative 2 right parenthesis over denominator negative 2 end fraction equals negative 1 A subscript 11 end subscript equals 0 comma A subscript 12 end subscript equals negative 1 comma A subscript 13 end subscript equals 0
    A subscript 21 end subscript equals negative 1 comma A subscript 22 end subscript equals 0 comma A subscript 23 end subscript equals 0
    A subscript 31 end subscript equals 0, A subscript 32 end subscript equals 0 comma A subscript 33 end subscript equals negative 1
    fraction numerator left parenthesis negative 1 right parenthesis to the power of 3 plus 2 end exponent M subscript 32 end subscript over denominator negative 2 end fraction comma text end text equals fraction numerator negative left parenthesis negative 2 right parenthesis over denominator negative 2 end fraction equals negative 1 blank A to the power of negative 1 end exponent equals fraction numerator a d j left parenthesis A right parenthesis over denominator vertical line A vertical line end fraction equals open square brackets table row 0 1 0 row 1 0 0 row 0 0 1 end table close square brackets equals A.

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