An **invertible matrix** (also known as a non-singular matrix or non-degenerate matrix) is a square matrix \( A \) that has an inverse. This means there exists another matrix \( B \) such that: \[ AB = BA = I \] where \( I \) is the identity matrix of the same dimension as \( A \). A matrix is invertible if and only if its determinant is non-zero (i.e.
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The set of all invertible matrices forms a group: the general linear group with matrix multiplication. Non-invertible matrices don't form a group due to the lack of inverse.