MathDB

Let

K

be a ring with unit and

M

the set of

2 \times 2

matrices constituted with elements of

K

. An addition and a multiplication are defined in

M

in the usual way between arrays. It is requested to: a) Check that

M

is a ring with unit and not commutative with respect to the laws of defined composition. b) Check that if

K

is a commutative field, the elements of

M

that have inverse they are characterized by the condition

ad - bc \ne 0

. c) Prove that the subset of

M

formed by the elements that have inverse is a multiplicative group.

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