Show that if the matrix A has the form $\begin{pmatrix}a &b\\ b& -a\end{pmatrix}$, so $ a^2+b^2= 1 $
112353
Prove that all 2x2 orthogonal matrices can be expressed as Rotation or Reflection
76188
Show $(W_1 + W_2 )^\perp = W_1^\perp \cap W_2^\perp$ and $W_1^\perp + W_2^\perp ⊆ (W_1 \cap W_2 )^\perp$
121982
Show matrix A is invertible if and only if $a_0 \neq 0$ with $A^n+a_{n-1}A^{n-1}+....+a_1A+a_0I=O$.
32103
Show that for a $2\times 2$ matrix $A^2=0$
88746
Positive definiteness of the matrix $A+B$
55056
To show: $\det\left[\begin{smallmatrix} -bc & b^2+bc & c^2+bc\\ a^2+ac & -ac & c^2+ac \\ a^2+ab & b^2+ab & -ab \end{smallmatrix}\right]=(ab+bc+ca)^3$
42500
Let $A$ and $B$ be matrices over $\mathbb C$. Then pick out the correct statements.
37985
Show that $|x|^2 = |y|^2$ with $A$ orthogonal and $Ax = \cos (θ)x − \sin (θ)y$, $Ay = \sin (θ)x + \cos (θ) y$
17032
If $ab=ba$, Prove $a^2$ commutes with $b^2$
152102
Prove that for every complex $2$x$2$ matrix $A$, there exists a matrix $X$ such that $X^3=A^2$.
98135
Show that the determinant of $A$ is equal to the product of its eigenvalues
155579
Show that $End_A(A)$ = {$r_a$ | $a ∈ A$}
58491
Proving the inverse of a matrix as a polynomial of matrices
140252
Matrices - Conditions for $AB+BA=0$
46831
Show that $ a，b, \sqrt{a}+ \sqrt{b} \in\mathbb Q \implies \sqrt{a},\sqrt{b} \in\mathbb Q $
128760
If $A$ and $B$ two $n\times n$ matrix such that $AB=BA$, then $\dim(A\cap B)$?
57543
Show that a matrix is nilpotent.