Given,

A be a 2 x 2 matrix with real entries such that A' = A + 1,

Now let

Now putting the value in A' = A + I we get,

Now equating both side we get,

.........(i)

b = c .... (ii) and c = b........(iii)

Now from equation (ii) & (iii) we get,

c = 0 or = ±l (not possible as mentioned in question)

c = 0

c = 0, b = 0

Also d = ad+l d=

Also given, |A 2 – A|= 4

Now let

So,t 2 (t-1) 2 = 4

t(t-1)=±2

t = 2 or t = -1

So, sum of all possible value will be

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