6 (10) Suppose that $A \in M_{m \times n}(\mathbb{R})$ and $\operatorname{rank}(A) = n$. Show that $A^T A \in M_{n \times n}(\mathbb{R})$ is an invertible matrix.
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6 (10) Suppose that $A \in M_{m \times n}(\mathbb{R})$ and $\operatorname{rank}(A) = n$. Show that $A^T A \in M_{n \times n}(\mathbb{R})$ is an invertible matrix.