Let $A\in M_{n,n}(\mathbb{C})$ be a diagonalisable matrix. Prove $\exists B \in M_{n,n}(\mathbb{C})$ such that $B^{2016} = A$
109167
Nth roots of square matrices
143354
Prove that there exists $c\in\mathbb{R}$ such that $f'(c)=f(c)$
114780
$\forall a,b,c \in \mathbb{N}\!:\ a\mid b \Rightarrow ac\mid bc. $ Divisibility Proof
64742
Prove a residue matrix $A$ (with coefficients in $\mathbb Z_n)$ has an inverse if and only if $\gcd(\det A,n) = 1$
33524
Prove the following $A \setminus (B\setminus C) = (A\setminus B)\cap (A \cup C)$
27248
If $A$ is an $m \times n$ matrix, prove that $Ax=0$ has infinite solutions $\iff$ $\text{rank}(A)<n$
4952
Let $A$ be a diagonalizable matrix and $\lambda$ be an eigenvalue of A. Prove that rank($\lambda I - A$) = rank(($\lambda I - A)^2$).
86841
Find a matrix $B$ such that $B^3 = A$
82410
Find $C$, if $A=CBC$, where $A$,$B$,$C$ are symmetric matrices.
158724
Show that $B$ is diagonalizable if If $AB=BA$ and $A$ has distinct real eigenvalues
64747
If $A^m=I$ then A is Diagonalizable
69980
Proving that if $A$ is an $n\times n$ orthogonal matrix, then $\det(A) = \pm1$
110944
Proving that $AB-BA=cI$ for nontrivial $c \in \mathbb{C}$
109745
If $(a,k)=(b,m)=1$, prove that $(ab,km)=(a,m)(b,k)$.
35757
A 2x2 matrix $M$ exists. Suppose $M^3=0$ show that (I want proof) $M^2=0$
1770
Matrix $M_1 = M(f', \mathcal{B}, \mathcal{B '})$ of $f$
49330
If for two suitable matrices $B$ and $C$, $AA^TB=AA^TC$ can we conclude that $A^TB=A^TC$?