grandes-ecoles 2014 QIV.A

grandes-ecoles · France · centrale-maths2__mp Matrices Determinant and Rank Computation

We denote by $\mathrm{GL}_2(\mathbb{Z})$ the set of invertible elements of the ring $\mathcal{M}_2(\mathbb{Z})$, equipped with its usual addition and multiplication.
Justify that an element $M$ of $\mathcal{M}_2(\mathbb{Z})$ belongs to $\mathrm{GL}_2(\mathbb{Z})$ if and only if $|\det M| = 1$.

We denote by $\mathrm{GL}_2(\mathbb{Z})$ the set of invertible elements of the ring $\mathcal{M}_2(\mathbb{Z})$, equipped with its usual addition and multiplication.

Justify that an element $M$ of $\mathcal{M}_2(\mathbb{Z})$ belongs to $\mathrm{GL}_2(\mathbb{Z})$ if and only if $|\det M| = 1$.

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.B.1 QII.B.2 QIII.A.1 QIII.A.2 QIII.B.1 QIII.B.2 QIII.B.3 QIII.B.4 QIII.C.1 QIII.C.2 QIV.A QIV.B QIV.C.1 QIV.C.2 QIV.C.3 QIV.C.4