$A$ is a $n\times n$ matrix and there exists a unique matrix $B$ such that $AB=I_n$. Prove that $BA=I_n$ and $B=A^{-1}$.
3301
If $AB = I$ then $BA = I$
27248
If $A$ is an $m \times n$ matrix, prove that $Ax=0$ has infinite solutions $\iff$ $\text{rank}(A)<n$
78224
Suppose $A$ is a general $n \times n$ matrix and $B$ is obtained by interchanging two rows of $A$. Prove that $\det(B) = -\det(A)$
118981
Proving $\sqrt{ab} = \sqrt a\sqrt b$
55062
$2\times 2$ matrix $C=AB-BA$
17032
If $ab=ba$, Prove $a^2$ commutes with $b^2$
8356
Any $n \times n$ matrix $A$ can be written as $A = B + C$ with $B$ is symmetric and $C$ skew-symmetric.
95227
Is the set of all $n\times n$ matrices, such that for a fixed matrix B  AB=BA, a subspace of the vector space of all $n\times n$ matrices?
145876
$AB-BA=A$ implies $A$ is singular and $A$ is nilpotent.
50266
In the following figure prove that: $AK||BC$
74460
Matrices A+B=AB implies A commutes with B
27474
A square matrix $n \times n$ is an invertible matrix iff the rank of the matrix is $n$.
120094
Prove, that for any A, B, C sets, $A\times (B\setminus C) = (A\times B)\setminus (A\times C)$ is true.
12927
$A^2+B^2=AB$ and $BA-AB$ is non-singular
61103
Prove that $\mathbb{|Q| = |Q\times Q|}$
55787
Is there any matrix $2\times 2$ such that $A\neq I$ but $ A^3=I$?
33477
Proving that if $A$ is a $8\times 8$ matrix over $\mathbb{R}$ and $A^3=A$, then $A$ is diagonalizable.