A matrix is invertible if it has an inverse matrix. The inverse matrix of a square matrix A, denoted as A^-1, is a matrix such that when the two matrices are multiplied, the result is the identity matrix, denoted as I. In other words, if A and B are matrices, AB = BA = I.

  For a matrix to be invertible, it must meet several conditions:

  1. The matrix must be square, meaning it has an equal number of rows and columns.

  2. The determinant of the matrix must not be zero. The determinant is a scalar value calculated from the elements of the matrix and is used to determine whether the matrix is invertible.

  3. The matrix must have full rank. This means that the rows or columns of the matrix are linearly independent, and there are no redundant rows or columns.

  If a matrix satisfies these conditions, it is said to be non-singular or invertible. Conversely, if a matrix does not meet these conditions, it is singular and does not have an inverse.

  The inverse of a matrix can be found using various methods, such as the Gaussian elimination method or the adjugate formula. Once the inverse is found, it can be used to solve linear systems of equations, calculate the inverse of another matrix, or perform other matrix operations.