Let $A$ be an $n \times n$ matrix. If $A$ is invertible, then $|A| \neq 0$?
101452
How is the determinant related to the inverse of matrix?
129564
Show that $A$ is an invertible matrix if $\left(A+I\right)^3=0$ and find $A^{-1}$
18585
Showing $A-I$ is invertible, when $A$ is a skew-symmetric matrix
82925
Let the matrix $A=[a_{ij}]_{n×n}$ be defined by $a_{ij}=\gcd(i,j )$. How prove that $A$ is invertible, and compute $\det(A)$?
55461
How to prove that if $a$ belongs to $\mathbb R$, such that $0\leq a \leq\epsilon$, then $a = 0$
124942
Prove that an upper triangular matrix is invertible if and only if every diagonal entry is non-zero.
150387
Questions about matrix rank, trace, and invertibility
51800
We have matrix $A\in M_{n-1\times n}(\mathbb Z)$ so that the sum of entries in each row is zero. Prove that $\det(AA^T)=nk^2.$
119301
Is the following matrix invertible?
25682
If $A$ is an $m\times n$ matrix, $B$ is an $n\times m$ matrix and $n<m$, then $AB$ is not invertible.
130268
How to prove that a nilpotent matrix is not invertible?
78224
Suppose $A$ is a general $n \times n$ matrix and $B$ is obtained by interchanging two rows of $A$. Prove that $\det(B) = -\det(A)$
73677
If the matrix $A^3 = 0$, is $A$ singular?
135316
A basic question on diagonalizability of a matrix
36567
$A^{T}A$ positive definite then A is invertible?
3038
For positive invertible operators $C\leq T$ on a Hilbert space, does it follow that $T^{-1}\leq C^{-1}$?
41411
How to show that the nth power of a $n \times n$ nilpotent matrix equals to zero $A^n=0$