a square matrix has an inverse iff
the determinant is nonzero
a square matrix has an inverse if and only if it is invertible.
A square matrix is invertible if its determinant is non-zero. In other words, if the determinant of the matrix is zero, then its inverse does not exist.
Another way to see if a matrix is invertible is to check if its columns or rows are linearly independent. If the columns or rows of the matrix are linearly dependent, then it is not invertible.
If a square matrix is invertible, then it has a unique inverse. The inverse of a matrix A is denoted by A^-1, and is such that A * A^-1 = A^-1 * A = I, where I is the identity matrix of the same size as A.
The inverse of a matrix can be found using various methods, such as Gaussian elimination, adjoint matrix, or using the formula A^-1 = (1/det(A)) * adj(A), where adj(A) is the adjoint matrix of A.
In summary, a square matrix has an inverse if and only if it is invertible, which means its determinant is non-zero, and its columns or rows are linearly independent.
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