$$A = \left( {\matrix{ a & c \cr c & b \cr } } \right)$$

$$|A| = ab - {c^2} = 2$$ ...... (1)

$$\left( {\matrix{ 2 & 1 \cr 3 & {{3 \over 2}} \cr } } \right)\left( {\matrix{ a & c \cr c & b \cr } } \right) = \left( {\matrix{ 1 & 2 \cr \alpha & \beta \cr } } \right)$$

$$2a + c = 1$$ ..... (2)

$$2c + b = 2$$ ..... (3)

$$3a + {3 \over 2}c = \alpha $$ .... (4)

$$3c + {3 \over 2}b = \beta $$ ..... (5)

From (1), (2) and (3)

$$a = {3 \over 4},b = 3,c = - {1 \over 2}$$

$$\Rightarrow$$ Now $$\alpha = {6 \over 4}$$

$$\beta = 3$$

$$s = {{15} \over 4}$$

$${{\beta s} \over {{\alpha ^2}}} = {{3 \times {{15} \over 4}} \over {{{\left( {{6 \over 4}} \right)}^2}}} = {{{{45} \over 4}} \over {{9 \over 4}}} = 5$$