Word Count : 164

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Define the action of (GL_2(\mathbb{R})) on (\mathbf{M}_2(\mathbb{R})) by [ A \cdot X = AX,\quad A \in GL_2(\mathbb{R}),\ X \in \mathbf{M}_2(\mathbb{R}). ] This is a well-defined group action since (I \cdot X = IX = X) and ((A_1A_2)\cdot X = A_1\cdot(A_2\cdot X)). ___ ______ _______ ________ _______ ________.
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