An invertible matrix is a square matrix that has an inverse, meaning it can be multiplied by another matrix to produce the identity matrix. In other words, the inverse of an invertible matrix is a matrix that, when multiplied by the original matrix, results in the identity matrix.
A matrix is invertible if its determinant is non-zero. The determinant is a scalar value that can be calculated from the elements of a square matrix. If the determinant is equal to 0, then the matrix is not invertible. However, if the determinant is non-zero, the matrix is invertible.
Invertible matrices are important in linear algebra because they allow for the solving of systems of linear equations. They also have many other applications in fields such as physics, engineering, and computer science.
The inverse of a matrix can be found using various methods, such as Gaussian elimination, Cramer's rule, and the adjugate matrix method. These methods involve manipulating the original matrix in a specific way to obtain the inverse matrix.
No, a non-square matrix cannot be invertible. In order for a matrix to have an inverse, it must be a square matrix, meaning it has an equal number of rows and columns. Non-square matrices do not have a determinant and therefore cannot have an inverse.