AP EAMCET202017 Sep 2020Morning ShiftMathematicsMatricesActual
The matrix (A= [ array cc 1 2 & 1 2 -1 2 & -1 2 array ] ) is
Options
- AUnitary
- BOrthogonal
- CNilpotent
- DInvolutory
Correct answer
C. Nilpotent
Step-by-step solution
( aligned A & = [ array cc 1 2 & 1 2 - 1 2 & - 1 2 array ] A^2 & = [ array cc 1 2 & 1 2 - 1 2 & - 1 2 array ] [ array cc 1 2 & 1 2 - 1 2 & - 1 2 array ] A^2 & = [ array cc 1 2 - 1 2 & 1 2 - 1 2 - 1 2 + 1 2 & - 1 2 + 1 2 array ] A^2 & = [ array ll 0 & 0 0 & 0 array ] null matrix aligned ) So, (A ) is nilpotent matrix