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AP EAMCET20226 Jul 2022Morning ShiftMathematicsMatricesActual

If A = [ array ll 3 & 4 5 & 6 array ] and B = [ array ll x & 0 0 & y array ], x , y N , then

Options

  1. AThere is exactly one such matrix B such that A B=I
  2. BThere is no matrix B such that AB = BA
  3. CThere exist only a finite number of matrices B such that AB = BA
  4. DThere exist infinite number of matrices B such that AB = BA

Correct answer

D. There exist infinite number of matrices B such that AB = BA

Step-by-step solution

We have aligned & A = [ array ll 3 & 4 5 & 6 array ] B = [ array ll x & 0 0 & y array ] x , y n & AB = [ array ll 3 & 4 5 & 6 array ] [ array ll x & 0 0 & y array ] & = AB = [ array ll 3 x & 4 y 5 x & 6 y array ] & = xy [ array ll 3 x & 4 y 5 x & 6 y array ] & now BA = xy [ array ll 3 & 4 5 & 6 array ] & Thus AB = BA aligned

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