What are the sufficient conditions to say $\det(A+B) = \det(A) + \det(B)$?
109573
Is sum of two orthogonal matrices singular?
106398
If $A$ is invertible show that $\det(A) \neq 0$
128760
If $A$ and $B$ two $n\times n$ matrix such that $AB=BA$, then $\dim(A\cap B)$?
10083
Determinant of matrix times a constant.
53101
Is it true that the relation |A| < |B| is a sufficient condition for claiming that $f$ is a bijection?
106305
Prove/disprove: if $\det(A+X) = \det(B + X)$ for all $X$, then $A=B$
63920
Does the fact that matrices $A, B$ are similar imply that $A+cI$ is similar to $B+cI$?
109312
How is the matrix identity $\det\begin{pmatrix}A&B\\B&A\end{pmatrix}=\det(A+B)\det(A-B)$ proved?
104068
Prove that $\forall a,b\in\mathbb{C} \exists c,d \in \mathbb{C}: c+d = a \land cd = b$
110703
How Can I prove (a+b) mod m = (a mod m) + (b mod m)) mod m?
84341
Can the determinant of a matrix can be made $0$?
150309
Why do we assume $a+b=b+a$ in a Ring with 1. Also, is it true with Rings without 1?
123483
Prove that $\operatorname{rank}(A) + \operatorname{rank}(B) \ge \operatorname{rank}(A + B)$
81181
Prove that $\det(M-I)=0$ if $\det(M)=1$ and $MM^T=I$
84522
A better proof for $\det(P) = \pm1$ if $P$ is an orthogonal matrix
81818
Prove or disprove : $\det(A^k + B^k) \geq 0$
127296
prove that a|b and b|a iff a=+-b