AP EAMCET202021 Sep 2020Evening ShiftMathematicsMatricesActual
If (A= [ array lll 3 & 0 & 0 0 & 5 & 0 0 & 0 & 4 array ] ) and (B=A^3 ), then (B⁻¹= )
Options
- A( [ array ccc -3 & 0 & 0 0 & -5 & 0 0 & 0 & -4 array ] )
- B( [ array ccc -27 & 0 & 0 0 & -125 & 0 0 & 0 & -64 array ] )
- C( [ array ccc 1 27 & 0 & 0 0 & 1 125 & 0 0 & 0 & 1 64 array ] )
- D( [ array ccc -1 27 & 0 & 0 0 & -1 125 & 0 0 & 0 & -1 64 array ] )
Correct answer
C. ( [ array ccc 1 27 & 0 & 0 0 & 1 125 & 0 0 & 0 & 1 64 array ] )
Step-by-step solution
The given matrix (A= [ array lll 3 & 0 & 0 0 & 5 & 0 0 & 0 & 4 array ] ) and ( aligned B & =A^3= [ array lll 3 & 0 & 0 0 & 5 & 0 0 & 0 & 4 array ] [ array lll 3 & 0 & 0 0 & 5 & 0 0 & 0 & 4 array ] [ array ccc 3 & 0 & 0 0 & 5 & 0 0 & 0 & 4 array ] & = [ array ccc 9 & 0 & 0 0 & 25 & 0 0 & 0 & 16 array ] [ array lll 3 & 0 & 0 0 & 5 & 0 0 & 0 & 4 array ]= [ array ccc 27 & 0 & 0 0 & 125 & 0 0 & 0 & 64 array ] & B⁻¹ & = 1 27 125 64 [ array ccc 125 64 & 0 & 0 0 & 27 64 & 0 0 & 0 & 527 125 array ] & = [ array ccc 1 27 & 0