Alternative proof: Matrix $A$ is similar to $B$ iff $\lambda I - A$ is equivalent to $\lambda I - B$
87265
If $(A-\lambda{I})$ is $\lambda$-equivalent to $(B-\lambda{I})$ then $A$ is similar to $B$
90475
Coordinate-free proof of $\operatorname{Tr}(AB)=\operatorname{Tr}(BA)$?
32767
Similar Matrices and Linear Transformations
116136
Proof that the inverse of a square matrix is unique
136329
A matrix is similar to its transpose
88349
Are the eigenvalues of $AB$ equal to the eigenvalues of $BA$? (Citation needed!)
35013
Demonstration: If all vectors of $V$ are eigenvectors of $T$, then there is one $\lambda$ such that $T(v) = \lambda v$ for all $v \in V$.
19203
Is the rank of a matrix the same of its transpose? If yes, how can I prove it?
145719
Similarity between $A$ and $B (2\times 2)$.
73155
Prove that for any square matrix, an invertible matrix B exists, so that BA is triangular
43310
Proving $A\cap(B-C)$ is equal to $(A\cap B)-(A\cap C)$
9574
How to show that $\det(AB) =\det(A) \det(B)$?
33448
Proof if $AB+BA=0$ Then atleast one of the matrices are singular.
130498
Linear algebra proof regarding matrices
79526
How do I tell if matrices are similar?
139685
If $A^2$ and $B^2$ are similar matrices, do $A$ and $B$ have to be similar?
1750
Fredholm alternative theorem for matrices