If $A$ and $B$ are $n×n$ matrices, $AB = -BA$ , and $n$ is odd, show that either $A$ or $B$ has no inverse.
33448
Proof if $AB+BA=0$ Then atleast one of the matrices are singular.
105921
Why do we have $ab=ba$?
10911
$A \in M_{n}(\mathbb{R})$ has inverse if and only if it's rank is n.
65432
Prove that every elementary matrix is invertible, and the inverse is again an elementary matrix.
41073
Prove $ax^2+bx+c=0$ has no rational roots if $a,b,c$ are odd
57543
Show that a matrix is nilpotent.
133482
$AB-BA$ is a nilpotent matrix if it commutes with $A$
84626
Why in these matrices are $AB=BA$ not equal? What is the logic behind them?
110502
$AB=BA$ with same eigenvector matrix
142980
If $\,A^k=0$ and $AB=BA$, then $\,\det(A+B)=\det B$
43570
Finding two non-zero matrices where $AX = BA$
99631
Prove/Disprove: Find $a\in S_4$ that is not a power of $b$ such that $ab=ba$ while $b=(123)$
33560
Show that matrices $A$ and $B$ commute if and only if $\begin{vmatrix} b & a-c \\ e & d-f\end{vmatrix}=0.$
145876
$AB-BA=A$ implies $A$ is singular and $A$ is nilpotent.
55062
$2\times 2$ matrix $C=AB-BA$
18585
Showing $A-I$ is invertible, when $A$ is a skew-symmetric matrix
121982
Show matrix A is invertible if and only if $a_0 \neq 0$ with $A^n+a_{n-1}A^{n-1}+....+a_1A+a_0I=O$.