> [!NOTE] Lemma > Let $I_{n}$ be a [[Real Identity Matrix|real identity matrix]] of order $n.$ Then its [[Left Multiplication Linear Map of Real Matrix|left multiplication linear map]] is the [[Identity Function|identity function]] $L_{I_{n}}:\mathbb{R}^{n}\to \mathbb{R}^{n}.$ **Proof**: Follows from [[Product with Real Identity Matrix]].