Let $A \in \mathbb{R}^{N \times N}$ be a D6160: Real square matrix such that
Let $m \in \{ 1, 2, \ldots, N \}$ be a D5094: Positive integer.
(i) | $N \in \{ 2, 3, 4, \ldots \}$ is a D5094: Positive integer |
(ii) | $\text{Cof}_A(i, j)$ is a D5941: Real square matrix cofactor for $A$ with respect to $(i, j)$ for each $i, j \in \{ 1, \ldots, N \}$ |
Then
(1) | \begin{equation} \text{Det} A = \sum_{n = 1}^N A_{m, n} \text{Cof}_A(m, n) \end{equation} |
(2) | \begin{equation} \text{Det} A = \sum_{n = 1}^N A_{n, m} \text{Cof}_A(n, m) \end{equation} |