Prove that matrix $A=c \cdot I$ where $I$ is an identity matrix
4280
A linear operator commuting with all such operators is a scalar multiple of the identity.
120010
Show that $\aleph_{\alpha}^{\aleph_{1}} = \aleph_{\alpha}^{\aleph_{0}}\cdot 2^{\aleph_1}$
40478
If $C$ commutes with certain matrices $A$ and $B$, why is $C$ a scalar multiple of the identity?
78224
Suppose $A$ is a general $n \times n$ matrix and $B$ is obtained by interchanging two rows of $A$. Prove that $\det(B) = -\det(A)$
76267
Prove that: $x_1\cdot x_2\cdots x_n>y_1\cdot y_2\cdots y_m$.
55056
To show: $\det\left[\begin{smallmatrix} -bc & b^2+bc & c^2+bc\\ a^2+ac & -ac & c^2+ac \\ a^2+ab & b^2+ab & -ab \end{smallmatrix}\right]=(ab+bc+ca)^3$
14277
Proving $f(x)=x\cdot |x|$ is a bijection
153506
Proving the inverse of a matrix equals $I_n-\frac{1}{n-1}A$
118304
If $A^2 = I$ (Identity Matrix) then $A = \pm I$
127127
Prove condition number of a invertible matrix is atleast one
137920
Proving an equation with invertible matrices
140400
Prove normal matrix is 4th power of some self-adjoint matrix
51321
Prove that $A = B = C = D$
65783
Proving: "The trace of an idempotent matrix equals the rank of the matrix"
26766
Proving : $A \cap (B-C) = (A \cap B) - (A \cap C)$
46106
Prove that $D_r \circ D_s = \{ (x,y) \in \mathbb{R}^2 \ | \ |x-y|<r+s \}$, where $D_a = \{ (x,y) \in \mathbb{R}^2\ | \ |x-y| < a \}$
129564
Show that $A$ is an invertible matrix if $\left(A+I\right)^3=0$ and find $A^{-1}$