Add, subtract, multiply, transpose, or find the determinant of matrices up to 5×5.
Matrix addition and subtraction work entry by entry, so A and B must have exactly the same number of rows and columns — there's no defined way to add entries that don't line up.
Each entry of A × B is a sum of products pairing a row of A with a column of B, so A's row length (its column count) must match B's column length (its row count) for every pairing to have a partner.
The determinant is only defined for square matrices (equal rows and columns) — it's a single number describing how that matrix scales area or volume, which only makes sense when rows and columns match up.