The statement in the title is not generally true, unless $C$ and $R$ have full rank. Then the $m$ by $r$ matrix $C$ is assumed to have $r$ independent columns (rank $r$). The $r$ by $n$ matrix $R$ is assumed to have $r$ independent rows (rank $r$). In this case the pseudoinverse $C^+$ is the left inverse of $C$, and the pseudoinverse $R^+$ is the right inverse of $R$

翻译：标题中的命题并非普遍成立，除非 $C$ 和 $R$ 具有满秩。此时假定 $m \times r$ 矩阵 $C$ 包含 $r$ 个独立列（秩为 $r$），而 $r \times n$ 矩阵 $R$ 包含 $r$ 个独立行（秩为 $r$）。在此情形下，伪逆 $C^+$ 是 $C$ 的左逆，伪逆 $R^+$ 是 $R$ 的右逆。