Definition: A non-singular matrix is a square matrix with a non-zero determinant that has an inverse.

Example: A practical application involving a colony of mole-rats demonstrates how matrices can model population changes.

Highlight: For 3x3 matrices, the inverse calculation involves finding the matrix of minors, cofactors, and the adjugate matrix.

Quote: "If A and B are non-singular matrices, then (AB)⁻¹ = B⁻¹A⁻¹"

Definition: A zero matrix is a matrix where all elements are zero, while an identity matrix has ones on the diagonal and zeros elsewhere.

Example: Matrix multiplication example: When multiplying matrices, the number of columns in the first matrix must equal the number of rows in the second matrix.

Highlight: Matrix multiplication is not commutative, meaning AB ≠ BA.

Vocabulary: Determinant (det) - a special number calculated from a square matrix that indicates whether the matrix is singular or non-singular.