1. The problem is to find the 3x3 identity matrix and understand its meaning. 2. The identity matrix, often denoted as $I_n$ for an $n \times n$ matrix, is a square matrix with 1's on the main diagonal and 0's elsewhere. 3. For a 3x3 identity matrix, it looks like this: $$I_3 = \begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix}$$ 4. Important rule: Multiplying any 3x3 matrix $A$ by $I_3$ leaves $A$ unchanged, i.e., $AI_3 = I_3A = A$. 5. This is because the identity matrix acts like the number 1 in multiplication but for matrices. 6. To understand easily, think of $I_3$ as a "do nothing" matrix that keeps other matrices the same when multiplied. 7. So, the 3x3 identity matrix is: $$\boxed{\begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix}}$$