NDA2019MathematicsMatricesActual
If A= [ array cc 1 & -1 -1 & 1 array ] , then the expression A ^3-2 ~A ^2 is
Options
- Aa null matrix
- Ban identity matrix
- Cequal to A
- Dequal to -A
Correct answer
A. a null matrix
Step-by-step solution
aligned & A= [ array cc 1 & -1 -1 & 1 array ] & A^2= [ array cc 1 & -1 -1 & 1 array ] [ array cc 1 & -1 -1 & 1 array ] & = [ array cc 2 & -2 -2 & 2 array ]=2 A & A^3-2 A^2=A A^2-2 A^2 & =A(2 A)-2(2 A) & =2 A^2-4 A & =2(2 A)-4 A & =4 A-4 A & =0 aligned