Matrix Formula

A matrix is a rectangular arrangement of numbers organized into rows and columns. Matrix formulas are used in algebra, statistics, computer science, engineering, and many other fields.

Matrix Addition

Matrices of the same dimensions can be added by adding corresponding entries.

Matrix Multiplication

For compatible matrices A and B, each entry of AB is found by multiplying entries from a row of A by the corresponding entries of a column of B and adding the products.

Determinant of a 2 × 2 Matrix

For A = [[a,b],[c,d]], the determinant is det(A) = ad − bc.

Inverse of a 2 × 2 Matrix

When ad − bc is not zero, the inverse is A⁻¹ = 1/(ad − bc) [[d,−b],[−c,a]].