f i n d space t h e space i n v e r s e space o f space minus open square brackets table row cell a plus i b space end cell cell c plus i d end cell row cell negative c plus i d end cell cell a minus i b end cell end table close square brackets space comma space space space space space space space space i f space a squared plus space b squared space plus space c squared space space plus d squared space space space equals space 1
also ,with  explanation

Asked by yash.bisht9910 | 25th Jun, 2015, 11:19: AM

Expert Answer:

C o n s i d e r space t h e space g i v e n space m a t r i x A equals open square brackets table row cell a plus i b end cell cell c plus i d end cell row cell negative c plus i d end cell cell a minus i b end cell end table close square brackets I f space A equals open square brackets table row w x row y z end table close square brackets space t h e n space A to the power of negative 1 end exponent equals fraction numerator 1 over denominator w z minus x y end fraction open square brackets table row z cell negative x end cell row cell negative y end cell w end table close square brackets H e r e comma space w equals a plus i b comma space x equals c plus i d comma space y equals negative c plus i d space a n d space z equals a minus i b T h u s comma space w z minus x y equals open parentheses a plus i b close parentheses open parentheses a minus i b close parentheses minus open parentheses c plus i d close parentheses open parentheses negative c plus i d close parentheses space space space space space space space space space space space space space space space space space space space space space space equals open parentheses a plus i b close parentheses open parentheses a minus i b close parentheses plus open parentheses c plus i d close parentheses open parentheses c minus i d close parentheses space space space space space space space space space space space space space space space space space space space space space space equals open parentheses a squared minus i squared b squared close parentheses plus open parentheses c squared minus i squared d squared close parentheses space space space space space space space space space space space space space space space space space space space space equals open parentheses a squared plus squared b squared close parentheses plus open parentheses c squared plus d squared close parentheses space space space space space space space space space space space space space space space space space space space space equals 1 space space space space space space open square brackets g i v e n space t h a t space a squared plus b squared plus c squared plus d squared equals 1 close square brackets T h u s space A to the power of negative 1 end exponent equals 1 over 1 open square brackets table row cell a minus i b end cell cell negative c minus i d end cell row cell c minus i d end cell cell a plus i b end cell end table close square brackets

Answered by Vimala Ramamurthy | 26th Jun, 2015, 09:48: AM