pöördmatrix
A pöördmatrix, also known as an inverse matrix in English, is a fundamental concept in linear algebra. Given a square matrix *A* of size *n × n*, its inverse, denoted as *A⁻¹*, is another square matrix such that when it is multiplied by *A*, the result is the identity matrix *I* of the same size. Mathematically, this relationship is expressed as *A⁻¹A = AA⁻¹ = I*. Not all matrices possess an inverse; those that do are called invertible or non-singular matrices.
The existence of an inverse is determined by the matrix's determinant. A matrix has an inverse if
*A⁻¹ = (1/det(A)) * [d -b; -c a],*
Inverses of matrices are widely used in solving systems of linear equations. If *Ax = b*, then multiplying
The concept of matrix inversion extends to other mathematical structures, including generalized inverses for non-square or