Let . Show that G is a group under matrix multiplication. Explain why each element of G has an inverse even though the matrices have 0 determinant.
Why isn't my latex code working? I want to produce a matrix with two rows, each rows with [ a a ]...
Let . Show that G is a group under matrix multiplication. Explain why each element of G has an inverse even though the matrices have 0 determinant.
Why isn't my latex code working? I want to produce a matrix with two rows, each rows with [ a a ]...
Let
We have
Comutativity:
Asociativity:
Then
Identity element:
Let be the identity element:
Then
We have
So the identity element is
Reciprocal element:
Let and the reciprocal element.
Then
So, the reciprocal element of is
Each element has an inverse because the identity element is not and we can't apply the same rule for an inverse of a matrix.