(50)

Given A = A -1

A = A.A -1 = I

.....(1)

ab+bd=0.....(2)

ac + cd = 0 ...(3)

bc + d 2 = 1 …(4)

(1)-(4) gives

a 2 -d 2 = 0

(a + d) = 0ora-d = 0

Case -I

a + d = 0 (a, d) = (-1, 1), (0, 0), (1, -1)

(a, d) = (-1, 1)

from equation (1)

1 + be = 1 bc = 0

b = 0 C = 12 possibilities

c = 0 b = 12 possibilities

but (0, 0) is repeated

2x12 = 24

24 - 1 (repeated) = 23 pairs

(a, d) = (1, -1) be = 0 23 pairs

(a, d) = (0, 0) be = 1

(b, c) = (1, 1) & (-1, -1), 2 pairs

Case - II

a = d

from (2) and (3)

a 0 then b=c=0

a 2 =1

(a, d) = (1,1), (-1,-1) 2 pairs

Total = 23 + 23 + 2 + 2

= 50 pairs

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