let $A$ be a matrix $m\times n$ if The colums of $A$ Span $\mathbb{R}^m$ then the equation $Ax=b$ will have an answer for all $b\in \mathbb{R}^m$
34536
Columns of matrix $A_{m \times n}$ span $\mathbb{R}^{m}$
123726
$2\times 2 $ matrices over $\mathbb{C}$ that satisfy $\mathrm A^3=\mathrm A$
28565
Prove $\operatorname{rank}A^TA=\operatorname{rank}A$ for any $A\in M_{m \times n}$
110381
Prove that if rank(A + B) = rank(A) + rank(B), then col(A) ∩ col(B) = {0}
32155
Prove that if for every $x \in \mathbb{R}^N$ $Ax=Bx$ then $A=B$
146847
Given a square matrix A of order n, prove $\operatorname{rank}(A^n) = \operatorname{rank}(A^{n+1})$
43570
Finding two non-zero matrices where $AX = BA$
24809
For all square matrices $A$ and $B$ of the same size, it is true that $(A+B)^2 = A^2 + 2AB + B^2$?
102299
Bijection between $\mathbb{R}^n$ and $\mathbb{R}^m$
135814
Prove certain subsets of $\mathbb R^n$ are subspaces
95227
Is the set of all $n\times n$ matrices, such that for a fixed matrix B  AB=BA, a subspace of the vector space of all $n\times n$ matrices?
36314
If $Ax = Bx$ for all $x \in C^{n}$, then $A = B$.
42500
Let $A$ and $B$ be matrices over $\mathbb C$. Then pick out the correct statements.
63036
Proving that $\dim(\mathrm{span}({I_n,A,A^2,...})) \leq n$
63183
Suppose $a,b,m,n$ are natural numbers, prove that if $a({m \over n})=b$ and $(a,n)=1$, then ${m \over n} \in \mathbb{N}$
57037
How does $(a,b)$ where $a,b\in \mathbb{Q}$ form a basis for $\mathbb{R}$?
147888
Show that $M=\bigcap_{\mathfrak{p}\in\operatorname{Spec}(R)}M_\mathfrak{p}=\bigcap_{\mathfrak{m}\in\text{Max}(R)}M_\mathfrak{m}$ for certain $M$.