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**Definition and Determinant of order 1 order 2**

**Determinant of order 3**

**Determinant calculation by sarrus diagram**

**Determinant of matrix order >=4**

**Definition and example**

**Definition**

**Let A be a square matrix of order n; then the sum of the product of elements of any row (column) with their cofactors is always equal to `|A|`**

**Let A be a square matrix of order n; then the sum of the product of elements of any row (column) with the cofactors of the corresponding elements of some other row (column) is 0.**

**Let A be a square matrix of order n then `|A| = |A^T|`**

**Let `A=[a_(ij)]` be a square matrix of order `n>=2` and let B be a matrix obtained from A by interchanging any two rows (columns) of A then `|B|=-|A|`**