grandes-ecoles 2013 QII.A.1

grandes-ecoles · France · centrale-maths2__pc Groups Group Homomorphisms and Isomorphisms
Show that for all $A$ in $\mathcal{M}_n(\mathbb{R})$ we have $A$ dos $A$, that for all $(A,B)$ in $\mathcal{M}_n(\mathbb{R})^2$ if $A$ dos $B$ then $B$ dos $A$, and that for all $(A,B,C)$ in $\mathcal{M}_n(\mathbb{R})^3$ if $A$ dos $B$ and $B$ dos $C$ then $A$ dos $C$. 
Show that for all $A$ in $\mathcal{M}_n(\mathbb{R})$ we have $A$ dos $A$, that for all $(A,B)$ in $\mathcal{M}_n(\mathbb{R})^2$ if $A$ dos $B$ then $B$ dos $A$, and that for all $(A,B,C)$ in $\mathcal{M}_n(\mathbb{R})^3$ if $A$ dos $B$ and $B$ dos $C$ then $A$ dos $C$.
Paper Questions
QI.A.1 QI.A.2 QI.A.3 QI.A.4 QI.B.1 QI.B.2 QI.C.1 QI.C.2 QI.C.3 QII.A.1 QII.A.2 QII.A.3 QII.A.4 QII.B.1 QII.B.2 QII.B.3 QIII.A.1 QIII.A.2 QIII.A.3 QIII.B.1 QIII.B.2 QIII.B.3 QIII.C QIII.D.1 QIII.D.2 QIII.D.3 QIII.E.1 QIII.E.2 QIII.E.3 QIII.E.4 QIV.A.1 QIV.A.2 QIV.A.3 QIV.A.4 QIV.A.5 QIV.A.6 QIV.B.1 QIV.B.2 QIV.B.3 QIV.B.4 QIV.B.5 QIV.C.1 QIV.C.2 QIV.C.3 QIV.D.1 QIV.D.2 QV.A.1 QV.A.2 QV.B.1 QV.B.2 QV.C.1 QV.C.2