# Cofactor matrix of a 4x4 matrix

Last updated: Jan. 2nd, 2019
Find the cofactor matrix of

### Proof

Let $M_{ij}$ be a submatrix given by removing $i$-th row and $j$-th column from $A$,

Each element of the cofactor matrix $\tilde{A}$ of $A$ is defined as

(Note that the subscript order of $M$ is different from that of $\tilde{A}$).
The determinant of $M_{ij}$ is respectively

(See

3x3 determinant).
Therefore,
each element of $\tilde{A}$ is

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