Prove that the matrix $(I-A)$ is invertible with $ \| (I-A)^{-1} \| \le \frac{1}{1-a}$.
42809
How can we show that $(I-A)$ is invertible?
55018
Prove that $A^*A + I$ is invertible
138342
Proof of a matrix exponential identity
24441
Inverse of a matrix is expressible as a polynomial?
22666
Proving that if $A^n = 0$, then $I - A$ is invertible and $(I - A)^{-1} = I + A + \cdots + A^{n-1}$
4952
Let $A$ be a diagonalizable matrix and $\lambda$ be an eigenvalue of A. Prove that rank($\lambda I - A$) = rank(($\lambda I - A)^2$).
144019
A strictly positive operator is invertible
119301
Is the following matrix invertible?
33030
Proof that $\inf A = -\sup(-A)$
11557
How to prove $\det(e^A) = e^{\operatorname{tr}(A)}$?
125195
If matrix A is invertible, is it diagonalizable as well?
78736
Check my proof that $(ab)^{-1} = b^{-1} a^{-1}$
64742
Prove a residue matrix $A$ (with coefficients in $\mathbb Z_n)$ has an inverse if and only if $\gcd(\det A,n) = 1$
115582
Prove that if a product$ AB$ of $n\times n$ matrices is invertible, so are the factors $A$ and $B$.
131480
Proof that composition of invertible linear transformations is invertible (without determinants)
60900
If $A^2=-I$, Prove that $\det{A}=1$
10042
How to Show that Linear transformation is invertible?