Homework Sourseif P0110 then P2017 aI bI c0201720170 dP eP if P0110 then P
if P=(0,-1;1,0), then P^2017 =?
a)I
b)-I
c)(0,-2017;2017,0)
d)-P
e)P
if P=(0,-1;1,0), then P^2017 =?
a)I
b)-I
c)(0,-2017;2017,0)
d)-P
e)P
if P=(0,-1;1,0), then P^2017 =?
a)I
b)-I
c)(0,-2017;2017,0)
d)-P
e)P
Solution
Given P=(0,-1;1,0).
Need to find P^2017
If P=0, P^2017 = (0)^2017 =0
Because \'0n\' is zero for any number.
If P=-1, P^2017 = (-1)^2017 =-1
Because in \'(-1)n\' if n is odd number then (-1)n =-1
if n is even number then (-1)n = 1
If P=1, P^2017 = (1)^2017 =1
Because (1)n = 1 for any \'n\'
So, if P=(0,-1;1,0), then P^2017 =(0,-1;1,0)
Therefore, P^2017 = P
Therefore, correct option is \'e\'
