If A and B are n×n matrices, then |A+B^T |=|A^T+B|
106511
Determinant of the sum of matrices: $\det (A + B^T) = \det(A^T + B)$
35080
If matrices $A$ and $B$ commute, $A$ with distinct eigenvalues, then $B$ is a polynomial in $A$
20878
If $(a,b)=1$ then prove $(a+b, ab)=1$.
33448
Proof if $AB+BA=0$ Then atleast one of the matrices are singular.
33560
Show that matrices $A$ and $B$ commute if and only if $\begin{vmatrix} b & a-c \\ e & d-f\end{vmatrix}=0.$
76335
Proving that two matrices are congruent, in order to establish a rank and signature result.
61538
Given a square matrix $A$, both $AA^T$ and $A^TA$ are symmetric
88746
Positive definiteness of the matrix $A+B$
17032
If $ab=ba$, Prove $a^2$ commutes with $b^2$
50939
If $A$ and $B$ are nonempty sets, prove that $A \times B = B \times A$ if and only if $A = B$
20110
How to prove $(AB)^T=B^T A^T$
75066
If the product of two square matrices is invertible, then both matrices are invertible
11895
If $AB=0$ prove that $\mathrm{rank}(A)+\mathrm{rank}(B)\leq n$
25357
Matrices $B$ that commute with every matrix commuting with $A$
141173
Are there matrices such that $AB=I$ and $BA \neq I$
125348
Does $\det(A + B) = \det(A) + \det(B)$ hold?
138707
show that if $a | c$ and $b | c$, then $ab | c$ when $a$ is coprime to $b$.