### 11.8.15 Determinant of a matrix in ℤ/pℤ

The det command finds the determinant of a matrix with elements in ℤ/pℤ. (See also Section 15.1.4.)

- det takes A, a matrix with elements in ℤ/pℤ.
- det(A) returns the determinant of A.

  Computations are done in ℤ/pℤ by Gaussian reduction.

#### Example

det([[1,2,9]%13,[3,10,0]%13,[3,11,1]%13])

or:

det([[1,2,9],[3,10,0],[3,11,1]]%13)

5%13 |  |  |  |  |  |  |  |  |  |

Hence, in ℤ/13ℤ, the determinant of M=[[1,2,9],[3,10,0],[3,11,1]] is 5%13 (in ℤ, det(M)=31).