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?