Prove that a 2 by 2 matrix C with tr(C)=0 can be written as C=AB-BA, where A and B are 2 by 2 matrices
55062
$2\times 2$ matrix $C=AB-BA$
115582
Prove that if a product$ AB$ of $n\times n$ matrices is invertible, so are the factors $A$ and $B$.
26766
Proving : $A \cap (B-C) = (A \cap B) - (A \cap C)$
43570
Finding two non-zero matrices where $AX = BA$
83475
Prove Or Disprove: tr(AB)=tr(A)*tr(B)
104124
Prove or disprove: $A-(B-C) = (A-B)-C$
55031
Show any matrix $A_{n\times n}$ can be written as sum of two nonsingular matrices
25870
Prove that $0 \leq ab + ac + bc - abc \leq 2.$
58491
Proving the inverse of a matrix as a polynomial of matrices
43310
Proving $A\cap(B-C)$ is equal to $(A\cap B)-(A\cap C)$
61274
If $AA^T$ is the zero matrix, then $A$ is the zero matrix
21726
Show that if $(b,c)=1$, then $(a,bc)=(a,b)(a,c)$.
128760
If $A$ and $B$ two $n\times n$ matrix such that $AB=BA$, then $\dim(A\cap B)$?
35897
Proof of: $AB=0 \Rightarrow Rank(A)+Rank(B) \leq n$
55056
To show: $\det\left[\begin{smallmatrix} -bc & b^2+bc & c^2+bc\\ a^2+ac & -ac & c^2+ac \\ a^2+ab & b^2+ab & -ab \end{smallmatrix}\right]=(ab+bc+ca)^3$
78224
Suppose $A$ is a general $n \times n$ matrix and $B$ is obtained by interchanging two rows of $A$. Prove that $\det(B) = -\det(A)$
109745
If $(a,k)=(b,m)=1$, prove that $(ab,km)=(a,m)(b,k)$.