Prove an eigenvector for two matrices is also the eigenvector for the product of those matrices.
33591
Product of two matrices sharing the same eigenvector
51967
Prove that if the sum of each row of $A$ equals $s$, then $s$ is an eigenvalue of $A$.
35080
If matrices $A$ and $B$ commute, $A$ with distinct eigenvalues, then $B$ is a polynomial in $A$
142640
Prove determinant of a matrix $=\prod_{j<i}(a_i-a_j)$
37162
Prove that matrices have equal rank.
48658
Let $A$ and $B$ be $n\times n$ matrices. Suppose $A$ is similar to $B$. Prove trace($A$) = trace($B$).
121253
Prove that any complex matrix can be expressed in term of Hermitian and anti-Hermitian matrices
36117
Prove that matrices of the form $\begin{pmatrix} x & x \\ x & x \end{pmatrix}$ are a group under matrix multiplication.
116376
Prove the determinant is the product of its diagonal entries
158845
Given $A$ and $B$ positive-definite matrices and $Q$ unitary matrix, prove that if $A = BQ$, then $A=B$.
59397
Eigenvalues of $AB$ and $BA$ where $A$ and $B$ are square matrices
63753
Eigenvalues of product of two complex matrices
123044
Commutative matrices are multiples of the identity
128990
Prove that, at least one of the matrices $A+B$ and $A-B$ has to be singular
7712
How to prove the both identity (matrix)
117769
How to show that the determinant of this matrix is in a nice product factorization,
98323
If A is invertible, prove that $\lambda \neq 0$, and $\vec{v}$ is also an eigenvector for $A^{-1}$, what is the corresponding eigenvalue?