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If [ array cc & & - array ] is to be the square root of two rowed unit matrix, then , and should satisfy the relation

Options

  1. A1+ ^2+ =0
  2. B1- ^2- =0
  3. C1- ^2+ =0
  4. D^2+ _ -1=0

Correct answer

B. 1- ^2- =0

Step-by-step solution

Since, [ array cc & & - array ] is a square root of I₂ i.e. two rowed unit matrix. [ array cc & & - array ]^2= [ array ll 1 & 0 0 & 1 array ] array ll & [ array ll 1 & 0 0 & 1 array ]= [ array cc & & - array ] [ array cc & & - array ] & [ array ll 1 & 0 0 & 1 array ]= [ array ll ^2+ & - - & + ^2 array ] array [ array ll 1 & 0 0 & 1 array ]= [ array cc ^2+ _ & 0 0 & ^2+ _ array ] aligned & ^2+ =1 & 1- ^2- =0 aligned

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