Invertible matrix: Suppose A is a

Suppose A is a square matrix. We look for an “inverse matrix” A−1 of the same size, such that A−1 times A equals I. Whatever A does, A−1 undoes. Their product is the identity matrix—which does nothing to a vector, so A−1Ax = x. But A−1 might not exist. Invertible matrices are defined as the matrix whose inverse exists. We define a matrix as the arrangement of data in rows and columns, if any matrix has m rows and n columns then the order of the matrix is m × n where m and n represent the number of rows and columns respectively. In this article, you will learn what a matrix inverse is, how to find the inverse of a matrix using different methods, properties of inverse matrix and examples in detail. Learn what makes a matrix invertible, how to check its determinant, and see stepwise examples. Get exam-ready with solved problems and quick tips on invertible matrices.