# Matrix permanent

## Permanent of a matrix

**2-by-2 matrix permanent formula **

`\text{perm}[[a,b],[c,d]] = ad + bc`

**3-by-3 matrix permanent formula **

`A = [[\color{blue}{a_11},a_12,a_13],[\color{blue}{a_21},a_22,a_23],[\color{blue}{a_31},a_32,a_33]]`

The permanent of A is equal to the sum of these 3 components, i.e.,

`\text{perm}(A) = \color{blue}{+a_(11)} * \text{perm}([[a_(22),a_(23)],[a_(32),a_(33)]]) \color{blue}{+a_(21)} * \text{perm}([[a_(12),a_(13)],[a_(32),a_(33)]]) \color{blue}{+a_(31)} * \text{perm} ([[a_(12),a_(13)],[a_(22),a_(23)]])`

So we get the following formula for a 3 × 3 matrix,

`\text{perm}(A) = \color{blue}{+a_(11)} * (a_(22)*a_(33) + a_(32) * a_(23)) \color{blue}{+a_(21)} * (a_(12) *a_(33) + a_(32)* a_(13)) \color{blue}{+a_(31)} * (a_(12)*a_(23) + a_(22)* a_(13) )`

## See also

Determinant of a Matrix

Linear algebra Calculators