A determinant, also referred to as the Jacobian Determinant, is the factor by which a given area increases or decreases.
Original shape:
Shape after transformation:
In this case, the determinant means how much did the area get stretched out compared to the original area.
The transformed shape is matrix 
which is a 2 x 2 matrix . Point (1,0) from the original shape moved to (3,0) and the point (0,1) from the original shape moved to (1,2).
How much bigger is the area of the transformed shape compared to the original shape? [hint] Count the squares and compare. It’s 6 times bigger. That means the determinant is 6.
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How to find the determinant using math:
The definition of the Determinant of a 2 x 2 Matrix
Subscript numbers: the first number is the row and the second number is the column.
The determinant of the matrix is given by det(A) = |A| = a11a22 – a21a12
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For matrix A, the determinant of matrix A is …
For A = , |A|=
= 3(2) – 0(1) = 6 – 0 = 6
The determinant of matrix A is 6
