How to prove matrix $A$ is invertible $\iff$ $\lambda=0$ is not an eigenvalue of $A$?
52208
Show that a matrix $A$ is singular if and only if $0$ is an eigenvalue.
127799
Eigenvalues of symmetric matrices are real without (!) complex numbers
119301
Is the following matrix invertible?
10001
Prove that the only eigenvalue of a nilpotent operator is 0?
64747
If $A^m=I$ then A is Diagonalizable
119387
If $A$ is any matrix then $A^*A$ and $AA^*$ are Hermitian with non-negative eigenvalues
118283
Show that if $A^{n}=I$ then $A$ is diagonalizable.
98135
Show that the determinant of $A$ is equal to the product of its eigenvalues
112701
Prove that if matrix $A$ is nilpotent, then $I+A$ is invertible.
127127
Prove condition number of a invertible matrix is atleast one
78307
Under what conditions is $AA^T$ invertible?
148946
If $\mathbf{A}$ is a $2\times 2$ matrix that satisfies $\mathbf{A}^2 - 4\mathbf{A} - 7\mathbf{I} = \mathbf{0}$, then $\mathbf{A}$ is invertible
141628
How did the equation $|A- \lambda I| = 0$ came for finding Eigen values of a Matrix
144019
A strictly positive operator is invertible
125195
If matrix A is invertible, is it diagonalizable as well?
14320
How to prove that eigenvectors from different eigenvalues are linearly independent
106398
If $A$ is invertible show that $\det(A) \neq 0$