Matrix Inversion

Inverse definition

An $(𝑛 \times 𝑛)$ square matrix $𝐴$ is called invertible (also nonsingular or nondegenerate) if there exists an $(𝑛 \times 𝑛)$ square matrix $𝐵$ such that:

$$𝐴𝐵 = 𝐵𝐴 = 𝐼_𝑛$$

• Here, $𝐼_𝑛$ denotes the $(𝑛 \times 𝑛)$ identity matrixa diagonal matrix where each element in the diagonal is equal to one. where we use ordinary matrix multiplication.

• If the matrix is invertible, then the matrix $𝐵$ is uniquely determined by $𝐴$ and is called the inverse of $𝐴$, denoted by $𝐴^{−1}$.