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AP EAMCET202422 May 2024Evening ShiftMathematicsMatricesActual

A= [ array lll 0 & 1 & 2 2 & 3 & 0 4 & 0 & 3 array ] and B is a matrix such that A B=B A . If A B is not an identity matrix, then the matrix that can be taken as B is

Options

  1. A[ array ccc -9 & -3 & 6 -6 & 8 & -4 12 & -4 & -2 array ]
  2. B[ array ccc 9 & -3 & 6 -6 & 8 & -4 -12 & -4 & 2 array ]
  3. C[ array ccc 9 & -3 & -6 -6 & 8 & -4 -12 & 4 & -2 array ]
  4. D[ array ccc 9 & -3 & -6 -6 & -8 & 4 -12 & 4 & -2 array ]

Correct answer

D. [ array ccc 9 & -3 & -6 -6 & -8 & 4 -12 & 4 & -2 array ]

Step-by-step solution

A = [ array lll 0 & 1 & 2 2 & 3 & 0 4 & 0 & 3 array ] and let B = [ array ccc x & y & z a & b & c u & v & w array ] Now AB = BA aligned & [ array lll 0 & 1 & 2 2 & 3 & 0 4 & 0 & 3 array ] [ array lll x & y & z a & b & c u & v & w array ]= [ array lll x & y & z a & b & c u & v & w array ] [ array lll 0 & 1 & 2 2 & 3 & 0 4 & 0 & 3 array ] & [ array ccc a+2 u & b+2 v & c+2 w 2 x+3 a & 2 y+3 b & 2 z+3 c 4 x+4 v & 4 y+3 v & 4 z+3 w array ]= [ array ccc 2 y+4 z & x+3 y & 2 x+3 z 2 b+4 c & a+3 b & 2 a+3 c 2 v+4 w & u+3 v

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