In $Ax=b$. If $A$ is not invertible there are no solutions or infinity. How to determine what the case is?
87387
Linear equations given by $Ax = b$ have a solution if and only if $\operatorname{rank}(A|b) = \operatorname{rank}(A)$
112428
Existence of least squares solution to $Ax=b$
3396
Find the case when $t^3$ never equals to any of the given
154327
$A^2X = X$ show that $AX = X$, if $A_{ij} > 0$ and $x_{i} > 0$
131844
When does $(e^a)^b = e^{ab}$ hold?
31898
Sufficient conditions for $x, Ax, A^2x, ...$ being linearly indepedent
125999
When does a system of equations have no solution?
13018
Why is $1^{\infty}$ considered to be an indeterminate form
121663
If $a$ is a zero divisor of $\mathbb{F}$, then does $a$ fail to have a multiplicative inverse?
158695
Prove that if $AB$ is invertible then $B$ is invertible.
130268
How to prove that a nilpotent matrix is not invertible?
86919
When (and more importantly, why) does $AA^T$ have an inverse?
36314
If $Ax = Bx$ for all $x \in C^{n}$, then $A = B$.
99631
Prove/Disprove: Find $a\in S_4$ that is not a power of $b$ such that $ab=ba$ while $b=(123)$
56171
Is $K(X)$ never algebraically closed?
8787
In a ring $(A,+, \cdot)$ if $aba = a$ then $bab = b$ and all non zero elements in $A$ are invertible.
86125
If $A$ is idempotent, then the eigenvalues of $A$ are $0$ or $1$