If matrix A = [ 0 1 , -1 1]

Question

find the value of p and q such that (pl+qA)^2 =A.

Answer 1

note that pI+qA =
(p q)
(-q p+q)
and that means that if you square that you get
(p^2-q^2 q(2p+q))
(-q(2p+q) p(p+2q))
so if you set that equal to A, you have
p^2-q^2 = 0
q(2p+q) = 1
p(p+2q) = 1
now just solve that for p and q.

Answer 2

So i got
p = +- q
Then
q = +-1/root3 , then p also same , when p = q

When p = - q, then q= +- i
Hence p = - + i

AM I RIGHT OR WRONG @oobleck

Answer 3

looks good to me.