Final answer:
The statement that if A and B are square matrices of the same size, then A + B is also a square matrix of the same size is True. Matrix addition of two matrices of the same dimensions results in another matrix of the same dimensions.
Step-by-step explanation:
If A and B are square matrices of the same size, then A + B is also a square matrix of the same size. This statement is True. The addition of two matrices is well-defined when the matrices have the same dimensions. When you add two square matrices, you add the corresponding entries of the matrices to get another matrix of the same dimensions. For example, if A and B are both 2x2 matrices:
A = |a11 a12| B = |b11 b12|
|a21 a22| |b21 b22|
The sum A + B will also be a 2x2 matrix:
A + B = |a11+b11 a12+b12|
|a21+b21 a22+b22|
Therefore, the result of adding two square matrices of the same size is another square matrix of that same size.