Let $A$ be an $n\times n$ matrix over real numbers such that $AB=BA,$ for all $n\times n$ matrices $B$
4280
A linear operator commuting with all such operators is a scalar multiple of the identity.
34536
Columns of matrix $A_{m \times n}$ span $\mathbb{R}^{m}$
108012
A matrix $M$ that commutes with any matrix is of the form $M=\alpha I$
21807
on proving bac-cab rule, $\vec{A} \times ( \vec{B} \times \vec{C})= \vec{B} (\vec{A} \cdot\vec{C})- \vec{C}(\vec{A}\cdot\vec{B})$
109745
If $(a,k)=(b,m)=1$, prove that $(ab,km)=(a,m)(b,k)$.
128990
Prove that, at least one of the matrices $A+B$ and $A-B$ has to be singular
13606
Prove that $K$ is isomorphic to a subfield of the ring of $n\times n$ matrices over $F$.
72092
If $A^2 = I$, $B^2=I$ and $(AB)^2=I$, then $AB = BA$
133482
$AB-BA$ is a nilpotent matrix if it commutes with $A$
25682
If $A$ is an $m\times n$ matrix, $B$ is an $n\times m$ matrix and $n<m$, then $AB$ 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 $\det(B) = -\det(A)$
15416
A weak converse of $AB=BA\implies e^Ae^B=e^Be^A$ from "Topics in Matrix Analysis" for matrices of algebraic numbers.
52040
"Inverse" of an $n\times k$ matrix.
12927
$A^2+B^2=AB$ and $BA-AB$ is non-singular
13026
Prove that if AB=I_m, then rk(A)=rk(B).
146243
Does there exist a matrix $\mathbf{A}\in\mathbb{R}^{3\times3}$ such that $\mathbf{A}^{2}=-\mathbf{I}$?
130498
Linear algebra proof regarding matrices