How $a+bi$ becomes $\left(\matrix{a & -b\\b & a}\right)$?
105727
Why is the complex number $z=a+bi$ equivalent to the matrix form $\left(\begin{smallmatrix}a &-b\\b&a\end{smallmatrix}\right)$
57318
Property of the conjugate transpose matrix with inner product
60006
Matrix equation: $A−A(A + B)^{−1}A = B−B(A + B)^{−1}B$
55056
To show: $\det\left[\begin{smallmatrix} -bc & b^2+bc & c^2+bc\\ a^2+ac & -ac & c^2+ac \\ a^2+ab & b^2+ab & -ab \end{smallmatrix}\right]=(ab+bc+ca)^3$
16382
Find $a$ such that $(x+a)(x+1991)+1=(x+b)(x+c)$ with $a,b,c\in\Bbb Z$
33559
Product or sum of invertible matrix give an invertible matrix?
3330
Square matrices, ABA = A?
63465
Orthogonal Projection of $ z $ onto the Affine set $ \left\{ x \mid A x = b \right\} $
37252
How can I show that $\begin{pmatrix} 1 & 1 \\ 0 & 1\end{pmatrix}^n = \begin{pmatrix} 1 & n \\ 0 & 1\end{pmatrix}$?
126018
Show that $ e^{A+B}=e^A e^B$
81868
How to prove $\operatorname{Tr}(AB) = \operatorname{Tr}(BA)$?
11388
How you get from $\gcd(a,b)=1 \Longleftrightarrow ax+by=1 \Longrightarrow a \nmid b$?
17430
If $\operatorname{rank}\left( \begin{bmatrix} A &B \\ C &D \end{bmatrix}\right)=n$ prove that $\det(AD)=\det(BC)$
18914
How prove this $A=\left(B-\frac{1}{110}I\right)^T\left(B+\frac{1}{110}I\right)$
129564
Show that $A$ is an invertible matrix if $\left(A+I\right)^3=0$ and find $A^{-1}$
142980
If $\,A^k=0$ and $AB=BA$, then $\,\det(A+B)=\det B$
9574
How to show that $\det(AB) =\det(A) \det(B)$?