Matrices with trace zero.
52928
If $\mathrm{Tr}(A)=0$ then $T=R^{-1}AR$ has all entries on its main diagonal equal to $0$
101631
Determinant of a finite-dimensional matrix in terms of trace
40222
Matrices that are not diagonal or triangular, whose eigenvalues are the diagonal elements
53032
Trace minimization when some matrix is unknown
98541
If a Matrix Has Only Zero as an Eigen-Value Then It Is Nilpotent
124090
zero matrix to the power of 0
140252
Matrices - Conditions for $AB+BA=0$
145157
Coordinate-Free Definition of Trace.
23224
$\mbox{rank}(A)=1$ implies $\det(A+I)=\mbox{trace}(A)+1$
26343
Number of certain (0,1)-matrices, Stanley's Enumerative Combinatorics
47829
Prove that $\operatorname{trace}(A^TA) = 0\ \iff\ A = 0$.
15197
Relation between trace and rank for projection matrices
133449
A proof that an orthogonal matrix with a determinant 1 is a rotation matrix
85845
Matrix with zeros on diagonal and ones in other places is invertible
94727
When the trace of the Frobenius homomorphism is zero?
65305
Minimal polynomial for an invertible matrix and its determinant
98646
Show determinant of matrix is non-zero