Let $\mathbb{R}^2$ with standard inner product space. Let $A \in \mathbb{R}^{2 \times 2}$ satisfies $\langle Ax, Ay \rangle= \langle x, y \rangle$ for every $x, y \in \mathbb{R}^2$, then $A$ is.... (triangle matrix, symmetry matrix, skew symmetry, diagonal, or orthogonal matrix?)
Actually I just learned about inner space product in linear algebra section. I am having no problem doing the exercise about it, but my friend gave me this problem. I read my textbook repeatedly, but didn't find any informations or example about matrix in inner product space form like it. Please, could you help me?