For example, matrix multiplication, if AB=AC or BA=CA and A is not equal to 0, you can get B=C, which is said to satisfy the law of elimination.

But in fact, if AB = AC and A is not equal to 0, B=C cannot be obtained.

This is because AD=0 can't get D=0, so AB=AC can only get A(B-C)=0, while B-C = 0 can't get B = C.

So matrix multiplication does not satisfy the law of elimination.