The ./ operator works just like / in most cases. The only exception is with matrices. The / command can't do anything with then (except for dividing a matrix by a value), but ./ will just apply the operation element-by-element. Obviously, when this is done for two matrices, their dimensions have to match up.
:[a,b;c,d] ./ [e,f;g,h] [a/e b/f] [c/g d/h]
When dividing a constant number by a matrix with ./, you may need to space it out so that there's no confusion between ./ and a decimal point.
:1./[a,b;c,d] Error: Data type :1 ./ [a,b;c,d] [1/a 1/b] [1/c 1/d]
240 - Dimension mismatch happens when dividing a matrix by another matrix of a different size.