Every square matrix is the sum of two invertible matrices, over any field
55031
Show any matrix $A_{n\times n}$ can be written as sum of two nonsingular matrices
65432
Prove that every elementary matrix is invertible, and the inverse is again an elementary matrix.
65305
Minimal polynomial for an invertible matrix and its determinant
4517
Showing a $2\times2$ matrix is invertible
25793
Extension fields isomorphic to fields of matrices
28861
Given an invertible matrix $A$ such that all elements in $A$ and in $𝐴^{−1}$ are integers, find $|𝐴^4|$
121047
Proof: Sum of dimension of orthogonal complement and vector subspace
33355
Proving that matrix in equation is invertible
123044
Commutative matrices are multiples of the identity
63007
Number of self-inverse matrices over prime field
90506
Finite multiplicative group of matrices with sum of traces equal to zero.
74341
Proving an invertible matrix which is its own inverse has determinant $1$ or $-1$
145447
bilinear form - proof
36613
Prove that simultaneously diagonalizable matrices commute
35625
Direct sum of orthogonal subspaces
57515
Similar matrices and field extensions
127764
Showing that $\mathbb{Q}[\sqrt{2}, \sqrt{3}]$ contains multiplicative inverses