grandes-ecoles 2016 QIII.A.2

grandes-ecoles · France · centrale-maths1__psi Matrices Determinant and Rank Computation
Prove that if $M \in \mathrm{O}_n(\mathbb{R})$, then its determinant equals 1 or $-1$. What do you think of the converse? 
Prove that if $M \in \mathrm{O}_n(\mathbb{R})$, then its determinant equals 1 or $-1$. What do you think of the converse?
Paper Questions
QI.A.1 QI.A.2 QI.A.3 QI.A.4 QI.B.1 QI.B.2 QII.A.1 QII.A.2 QII.A.3 QII.B.1 QII.B.2 QII.B.3 QII.B.4 QIII.A.1 QIII.A.2 QIII.A.3 QIII.B.1 QIII.B.2 QIII.B.3 QIII.B.4 QIII.C QIV.A.1 QIV.A.2 QIV.A.3 QIV.A.4 QIV.A.5 QIV.A.6 QIV.A.7 QIV.B.1 QIV.B.2 QIV.B.3 QIV.B.4 QIV.B.5 QIV.B.6