AP EAMCET2012MathematicsMatrices
A= [ array rr i & -i -i & i array ], B= [ array rr 1 & -1 -1 & 1 array ] A^8
Options
- A4 B
- B8 B
- C64 B
- D128 B
Correct answer
D. 128 B
Step-by-step solution
Given, A= [ array rr i & -i -i & i array ] and B= [ array rr 1 & -1 -1 & 1 array ] aligned A^2 & = [ array rr i & -i -i & i array ] [ array rr i & -i -i & i array ] & = [ array rr i^2+i^2 & -i^2-i^2 -i^2-i^2 & i^2+i^2 array ] & = [ array rr -1-1 & 1+1 1+1 & -1-1 array ]= [ array rr -2 & 2 2 & -2 array ]=-2 B B^2 & = [ array rr 1 & -1 -1 & 1 array ] [ array rr 1 & -1 -1 & 1 array ] & = [ array rr 1+1 & -1-1 -1-1 & 1+1 array ]= [ array rr 2 & -2 -2 & 2 array ] & =2 B aligned aligned & Now, A^8= (A^2 )^4=(-2 B)^4 & =1