Final answer:
A matrix does not have to be square to use row operations; such operations can be applied to any matrix to solve systems of linear equations or to simplify the matrix.
Step-by-step explanation:
It is false that a matrix must be square to solve using row operations. Row operations can be used on any matrix to solve a system of linear equations, regardless of whether it is square. Matrices that are not square are often associated with systems that are either over-determined or under-determined, and row operations are a tool for finding solutions or identifying if solutions exist.
Row operations can also be used to simplify matrices to reach echelon form or reduced echelon form, which helps in understanding the solution set of the system.