本文首先介绍了逆矩阵的定义以及逆矩阵的相关性质。其次，根据逆矩阵的相关理论主要介绍了矩阵求逆的几种常用方法。 如定义法、伴随矩阵法、初等变换法、三角分解法、分块矩阵法等,并运用软件matlab7.0对一些方法实现了程序化。且通过多次检验证明了所编程序的正确性。文章最后简要阐述了对一些特殊矩阵的求逆算法（如对称正定矩阵、有理矩阵），还有针对一般矩阵的广义逆矩阵的作了浅层次的探究。-This paper introduces the definition of the relevant properties of the inverse matrix and inverse matrix. Secondly, according to the theory of inverse matrix describes several methods for matrix inversion. As defined in law, with matrix method, elementary transformation, triangular decomposition, block matrix method, and use the software on some of the ways to achieve a matlab7.0 procedures. And through a number of tests to prove the correctness of the compiled program. Finally, the article briefly describes some of the special matrix inversion algorithm (eg symmetric positive definite matrix, rational matrix), there were shallow explore generalized inverse matrix for general matrices.