1. The problem states: If the products $AB$ and $BA$ are defined, then $AB$ and $BA$ are square matrices. 2. To understand this, recall the rule for matrix multiplication: For two matrices $A$ and $B$, the product $AB$ is defined if the number of columns of $A$ equals the number of rows of $B$. 3. Suppose $A$ is an $m \times n$ matrix and $B$ is a $p \times q$ matrix. 4. For $AB$ to be defined, $n = p$. 5. For $BA$ to be defined, $q = m$. 6. Therefore, $AB$ is an $m \times q$ matrix and $BA$ is a $p \times n$ matrix. 7. Since $n = p$ and $q = m$, then $AB$ is $m \times m$ and $BA$ is $n \times n$. 8. Both $AB$ and $BA$ are square matrices because their dimensions are $m \times m$ and $n \times n$ respectively. 9. Hence, the statement is True.