We know that the KroneckerProduct of two matrices a and b will be done as
a = {{2, 1}, {I, 3}}; b = {{2, 3, 1}, {1, 4, 6}, {2, 4, 6}};
m=KroneckerProduct[a,b]
(**{{4, 6, 2, 2, 3, 1}, {2, 8, 12, 1, 4, 6}, {4, 8, 12, 2, 4, 6}, {2 I,
3 I, I, 6, 9, 3}, {I, 4 I, 6 I, 3, 12, 18}, {2 I, 4 I, 6 I, 6, 12,
18}}**
Is there any defined reverse procedure by which if we have a given matrix such as m we be able to access a and b?!