If , verify that (AB)–1 = B–1A–1.

Asked by Topperlearning User | 3rd May, 2016, 05:03: PM

Expert Answer:

Here,

,
Co-factors of elements of AB,
N o w comma space B to the power of negative 1 end exponent A to the power of negative 1 end exponent equals 1 over 20 open square brackets table row 5 0 row cell negative 2 end cell 4 end table close square brackets times fraction numerator 1 over denominator negative 4 end fraction open square brackets table row 0 cell negative 1 end cell row cell negative 4 end cell 3 end table close square brackets
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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 fraction numerator 1 over denominator negative 80 end fraction open square brackets table row cell 0 minus 0 end cell cell negative 5 plus 0 end cell row cell 0 minus 16 end cell cell 2 plus 12 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 equals fraction numerator 1 over denominator negative 80 end fraction open square brackets table row 0 cell negative 5 end cell row cell negative 16 end cell 14 end table close square brackets
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H e n c e comma space open parentheses A B close parentheses to the power of negative 1 end exponent equals B to the power of negative 1 end exponent A to the power of negative 1 end exponent

Answered by  | 3rd May, 2016, 07:03: PM