Find Determinants using montante (bareiss algorithm) ...
`[[3,2,4],[2,0,2],[4,2,3]]`

Solution:

`A`

=

`3` `2` `4` `2` `0` `2` `4` `2` `3`

Step-0: Previous Pivot `=1`

Step-1: Pivot `=A_(1,1)=3`, Previous Pivot `=1`

`A_(i,j)=(A_(1,1) * A_(i,j) - A_(i,1) * A_(1,j))/(1)`, where `i>1` and `j>1`

`A_(2,2)=(3 * 0 - 2 * 2)/(1)=-4`

`A_(2,3)=(3 * 2 - 2 * 4)/(1)=-2`

`A_(3,2)=(3 * 2 - 4 * 2)/(1)=-2`

`A_(3,3)=(3 * 3 - 4 * 4)/(1)=-7`

So matrix becomes

`A`

=

`3` `2` `4` `2` `-4` `-2` `4` `-2` `-7`

Step-2: Pivot `=A_(2,2)=-4`, Previous Pivot `=3`

`A_(i,j)=(A_(2,2) * A_(i,j) - A_(i,2) * A_(2,j))/(3)`, where `i>2` and `j>2`

`A_(3,3)=(-4 * -7 - -2 * -2)/(3)=8`

So matrix becomes

`A`

=

`3` `2` `4` `2` `-4` `-2` `4` `-2` `8`

Determinant will be `A_(3,3)` multiplied by the scaling factor 1

`:.` Determinant `=8`

---