Show that $\exists $ a $3\times 3$ invertible matrix $M\neq I_3$ with entries in $\mathbb Z_2$ such that $M^7=I_3$.
141105
Show that there exists a $3 × 3$ invertible matrix $M$ with entries in $\mathbb{Z}/2\mathbb{Z}$ such that $M^7 = I_3$.
73697
Let $A, B$ be $n\times n$ with $n\ge 2$ nonsingular matrices with real entries such that $A^{-1} + B^{-1} =(A+B)^{-1}$
44307
Prove $\sqrt[3]{3} \notin \mathbb{Q}(\sqrt[3]{2})$
30752
Proof of $(\mathbb{Z}/m\mathbb{Z}) \otimes_\mathbb{Z} (\mathbb{Z} / n \mathbb{Z}) \cong \mathbb{Z}/ \gcd(m,n)\mathbb{Z}$
108012
A matrix $M$ that commutes with any matrix is of the form $M=\alpha I$
75215
Properties of invertible matrices
110256
Let $a,b \in {\mathbb{Z_+}}$ such that $a|b^2, b^3|a^4, a^5|b^6, b^7|a^8 \cdots$, Prove $a=b$
46110
how many 2x2 matrices are invertible in mod p
82925
Let the matrix $A=[a_{ij}]_{n×n}$ be defined by $a_{ij}=\gcd(i,j )$. How prove that $A$ is invertible, and compute $\det(A)$?
109217
Invertibility of the Product of Two Matrices
27474
A square matrix $n \times n$ is an invertible matrix iff the rank of the matrix is $n$.
148946
If $\mathbf{A}$ is a $2\times 2$ matrix that satisfies $\mathbf{A}^2 - 4\mathbf{A} - 7\mathbf{I} = \mathbf{0}$, then $\mathbf{A}$ is invertible
25488
Let $A,B$ be $m\times m$ matrices such that $AB$ is invertible. Show $A,B$ invertible.
86841
Find a matrix $B$ such that $B^3 = A$
95103
A rational matrix such that $A^{2017}=I_n$
18585
Showing $A-I$ is invertible, when $A$ is a skew-symmetric matrix
119052
Finding invertible elements in $\mathbb{Z}/m\mathbb{Z}$