Homography Matrix Correlations
Consider three points $A$ in image 1,$B$ in image 2 and $C$ in image 3.$H1$ is the homography matrix from $A$ to $B$ and $H2$ is the homography matrix from $B$ to $C$.
Then,

$$B = H1A$$

$$C = H2B$$

Substituting for B from first equation

$$C = H2(H1A)$$

Due to matrix associative property,

$$C = (H2H1)A$$

The homography matrix from $A$ to $C$ is given by $H2H1$.