Prove that for the $\mathbb R^{n\times n}$ vector space doesn't exist a basis from $n^2$ matrices, such that AB=BA for every two matrices in base.
25430
When is matrix multiplication commutative?
26497
Take $\mathbb{R}$ as a vector space over $\mathbb{Q}$, then a basis for $\mathbb{R}$, then $|B|=2^{\aleph_0}$
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 $\det(AA^T)=nk^2.$
110944
Proving that $AB-BA=cI$ for nontrivial $c \in \mathbb{C}$
84871
Determining the dimension of span$\{AB-BA : A,B \in M_{n \times n}(\mathbb R) \}$
123505
how to prove vector norm equivalence in finite dimensional space($\mathbb{R}^{n}$)?
133087
Prove that, if $\{u,v,w\}$ is a basis for a vector space $V$, then so is $\{u+v, v+w, u+v+w\}$.
86749
Prove that any set of vectors $S \subset \mathbb{R}^n$ containing the zero vector cannot be linearly independent
56102
Prove that there is no non-zero linear operator on $\mathbb C^{2}$ such that $(\alpha | T\alpha) = 0$
57037
How does $(a,b)$ where $a,b\in \mathbb{Q}$ form a basis for $\mathbb{R}$?
43282
Why do $n$ linearly independent vectors span $\mathbb{R}^{n}$?
57649
Prove that for every $f$, a bilinear form, there exists a basis ${v_1,...,v_n}$ so that $f(v_i,v_j) = -f(v_j,v_i)$
62065
Prove that $v_1, \dots v_n$ is a basis of V.
114250
If $V_0$ is the subspace of matrices of the form $C=AB-BA$ for some $A,B$ in a vector space $V$ then $V_0=\{A\in V|\operatorname{Trace} (A)=0\}$
116273
Does every $\mathbb{R},\mathbb{C}$ vector space have a norm?
70576
Elementary proof that $\mathbb{R}^n$ is not homeomorphic to $\mathbb{R}^m$
116823
VERIFYING: Proving an $n \times n$ Matrix Vector Space