Determinants are special numbers you can find from a square matrix. They tell us important things about that matrix.

Here’s some simple ways to think about determinants:

• What They Mean Geometrically:
  • If you have a $2 \times 2$ matrix, the determinant shows the area of a shape called a parallelogram. This shape is made by the two column vectors of the matrix.
  • If you have a $3 \times 3$ matrix, the determinant gives us the volume of a shape called a parallelepiped, which is a 3D version of the parallelogram.

So, the determinant is helpful because it connects math concepts to shapes we can visualize in real life!