How to denote that two matrices have the same size, without using notation for the number of rows and columns?

Question

How can I write that a matrix, e.g., $A_{p×q}$ has the same size as matrix $B_{m×n}$, i.e. $p=m$ and $q=n$, without using variables $p,q,m,n$, just the symbols for $A$ and $B$?

Answer 1

What's wrong with "$A$ and $B$ have the same dimensions"? Math writing is invented and used for the sake of communication, so if words can explain something in a short, concise and precise way, why make it more difficult than it has to?

If you have a need to write that phrase a lot of times in a relatively small amount of text, you could define a symbol for it, if you'd like. But that's up to you.