The operator space has square dimension

Let V be a vector space over $\mathbb{R}$. Let $T_{1}, T_{2} : V \to V$ be two $\mathbb{R}-$linear transformations such that $T_{1} + T_{2}$ and $T_{1} - T_{2}$ are linearly independent over $\mathbb{R}$. Consider the following statements: (A) The transformations $T_{1}$ and $T_{2}$ are linearly independent over $\mathbb{R}. (B)$ There exist $\mathbb{R}-$linear transformations $T_{3}, T_{4} : V \to V$ such that {$T_{1} + T_{2}, T_{1} - T_{2}, T_{3}, T_{4}$} is linearly independent over $\mathbb{R}$. Which of the following statements is true?