Question

Punctul c) de la ex 1
Mulțumesc !

Answer 1

X ∈ M₂ ⇒ $\left[\begin{array}{ccc}m&n\\an&m+bn\end{array}\right]$

A · X = $\left[\begin{array}{ccc}an&m+bn\\a(m+bn)&an+b(m+bn)\end{array}\right]$, ∨ m, n ∈ Z (1)

X · A = $\left[\begin{array}{ccc}an&m+bn\\a(m+bn)&an+b(m+bn)\end{array}\right]$, ∨ m, n ∈ Z (2)

Deci, din (1)  si (2) ⇒ A· X = X·A , m, n E Z