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Explanation:

S[M(D(A(a,b),2),D(A(a,b),2)),M(D(S(a,b),2), D(S(a, b),2))]

= S[M(D((a + b),2),D((a + b),2)),M(D((a – b),2),

D((a – b),2))] = $S\left[M\left\{\frac{(a+b)}{2},\frac{(a+b)}{2}\right\},M\left\{\frac{(a-b)}{2},\frac{(a-b)}{2}\right\}\right]$

$=S\left[{\left\{\frac{(a+b)}{2}\right\}}^2,{\left\{\frac{(a-b)}{2}\right\}}^2={\left\{\frac{(a+b)}{2}\right\}}^2-{\left\{\frac{(a-b)}{2}\right\}}^2\right]$

= $\frac{4ab}{2}=ab$