AP EAMCET202315 May 2023Morning ShiftMathematicsDeterminantsActual
If A= [ array cc i & 0 0 & -i array ], B= [ array cc 0 & -1 1 & 0 array ] and C= [ array ll 0 & i i & 0 array ] , then
Options
- AA ^2+ B ^2+ C ^2=3 ~A ^2 ~B ^2 C ^2
- BA ^2+ B ^2+ C ^2=3 ABC
- CA ^2+ B ^2+ C ^2=3 I
- DA ^2+ B ^2+ C ^2=2 ABC
Correct answer
A. A ^2+ B ^2+ C ^2=3 ~A ^2 ~B ^2 C ^2
Step-by-step solution
aligned & A ^2= A A = [ array cc -1 & 0 0 & -1 array ], B ^2= B B = [ array cc -1 & 0 0 & -1 array ] & C ^2= C C = [ array cc -1 & 0 0 & -1 array ] aligned Hence, aligned & A^2+B^2+C^2= [ array cc -3 & 0 0 & -3 array ] & and 3 ~A ^2 ~B ^2 C ^2=3 [ ( ~A ^2 ~B ^2 ) C ^2 ] & =3 [ array cc -1 & 0 0 & -1 array ]= [ array cc -3 & 0 0 & -3 array ] & A ^2+ B ^2+ C ^2=3 ~A ^2 ~B ^2 C ^2 & aligned