$\operatorname{span}\{AB-BA : A, B \in M_n(\Bbb R)\}$ is the set of all matrices with trace $0$
57070
Dimensionality of null space when Trace is Zero
58595
Existence of a G-invariant matrix
106986
Eigenvalues of $AB$ and $BA$
117737
Why is $\mathfrak{sl}(n)$ the algebra of traceless matrices?
8291
If $n$ vectors are linearly independent, is their span $\mathbb{R}^n$?
129743
$A$ be a $2\times 2$ real matrix with trace $2$ and determinant $-3$
73286
Show that the set of all symmetric, real matrices is a subspace, determine the dimension
66709
Are the matrix products $AB$ and $BA$ similar?
150228
If $E$ has eigenvalues $\lambda_1, \ldots, \lambda_n$, then $B \mapsto [E,B] = EB - BE$ has eigenvalues $\lambda_i - \lambda_j$.
41611
Open and closed set in n by n matrices space.
34536
Columns of matrix $A_{m \times n}$ span $\mathbb{R}^{m}$
105996
Topology of matrices
62474
If $AB=I_n$ and $BA=I_m$ then $n=m$.
51889
How to "find" this Lie algebra: proof that $\mathfrak{sl}$ is trace zero matrices
142863
Show that every ideal of the matrix ring $M_n(R)$ is of the form $M_n(I)$ where $I$ is an ideal of $R$
35801
Traceless matrices and commutators
142363
The determinant of a block Matrix of Order $2n$