Matrix: If A∧2=A, then A=0 or a = e, why is it wrong?

If the square of matrix A is equal to A, then matrix A=0 or matrix A=E, the condition of this proposition is that matrix A or A-E is reversible.

Matrix a is an n-order square matrix. If there is an n-order matrix b, so that the product of matrices A and B is identity matrix, then A is called invertible matrix, and B is the inverse matrix of A. If the inverse matrix of a square matrix exists, it is called invertible matrix or nonsingular matrix, and its inverse matrix is unique.

Generally speaking, pseudo-inverse refers to Moore-Penrose generalized inverse, which was independently proposed by Moore and roger penrose.

Reversible matrix calculation:

Gauss elimination is the most classic and famous method of matrix inversion, but gauss elimination is rarely used to solve the inverse matrix in practical application.

Gaussian elimination has two versions: row transformation version and column transformation version, and row transformation is more widely used in daily applications. These two basic principles are the same. Gaussian elimination first connects matrix A with identity matrix I to form a new augmented matrix.