Understand zero and identity matrices

What you'll learn

1. Identify the zero matrix $O$ and explain its role as the additive identity for matrix addition.
2. Construct the identity matrix $I_n$ and verify $AI = IA = A$ for a given square matrix.
3. Compute the determinant of a $2 \times 2$ matrix using $\det(A) = ad - bc$.
4. State and apply the theorem: a square matrix has a multiplicative inverse if and only if its determinant is nonzero.
5. Compute the inverse of an invertible $2 \times 2$ matrix and verify $AA^{-1} = I$.

Prerequisites

• Add, subtract, and multiply matrices
• Understand matrix multiplication properties