若方块矩阵满足条件，则称为非奇异方阵，否则称为奇异方阵。

阶方阵是非奇异方阵的充要条件是可逆，即可逆方阵就是非奇异方阵。

对一个阶方阵，如果存在一个阶方阵使（是单位矩阵），则称是可逆的，也称为非奇异矩阵。是的逆阵。

给定一个阶方阵，则下面的叙述都是等价的：

In linear algebra, an n-by-n square matrix A is called invertible (also nonsingular or nondegenerate) if there exists an n-by-n square matrix B such that

where I_n denotes the n-by-n identity matrix and the multiplication used is ordinary matrix multiplication. If this is the case, then the matrix B is uniquely determined by A and is called the inverse of A, denoted by A.