Determinant
A scalar value calculated from the elements of a square matrix. It provides important information about the matrix, such as whether it has an inverse.
If the determinant is 0, the matrix is singular (no inverse).
|A| = a11a22 - a12a21
Inverse Matrix
Given a square matrix A, the inverse matrix A-1 is the matrix such that when multiplied by A, it results in the Identity matrix.
A-1 = (1 / |A|) × adj(A)
Transpose
The transpose of a matrix is an operator which flips a matrix over its diagonal. Rows become columns, and columns become rows.
(AT)ij = Aji