Question

Let $G = left{ egin{pmatrix} a & -b \ b & a end{pmatrix} mid a, b in mathbb{R} ext{ with } a eq 0 ext{ or } c eq 0 ight}$. Show that $G$ is a group under matrix multiplication (You have to give the inverse of an element).

          Let $G = left{ egin{pmatrix} a & -b \ b & a end{pmatrix} mid a, b in mathbb{R} 	ext{ with } a 
eq 0 	ext{ or } c 
eq 0 
ight}$.
Show that $G$ is a group under matrix multiplication (You have to give the inverse of an element).

Added by Alejandro M.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Madhur L

08/01/2023

Step 1

Closure: We need to show that the product of any two elements in G is also in G. Let A = [a c; 0 b] and B = [x y; 0 z] be two elements in G. Then, AB = [ax cz+by; 0 bz] is also in G since a, b, c, x, y, and z are all real numbers and a and c are not both zero. Show more…

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Let G = { (a -b / b a) | a,b ∈ ℝ with a ≠ 0 or c ≠ 0}. Show that G is a group under matrix multiplication (You have to give the inverse of an element).