# Determinant and Other Properties

## `Determinant(A: parameters): MtrxSprs -> RngElt`

```magma
MonteCarloSteps: RngIntElt                    Default: 
```

Given a square sparse matrix $A$ over the ring $R$, return the determinant of $A$ as an element of $R$. $R$ may be any commutative ring. The algorithm first performs sparse elimination using Markowitz pivoting ([[Duff *et al.*, 1984](../../references.md#cite-smatbook), Sec. 9.2]) to obtain a smaller dense matrix, then the determinant algorithm for dense-representation matrices is applied to this matrix. If the parameter `MonteCarloSteps` is given, then this is passed to the dense algorithm for the dense matrix.