Question

Which of the following are the subgroups?
a) The set of all nxn matrices with determinant 2
b) The set of all upper triangular nxn matrices with no zeros on the diagonal
c) The set of all nxn matrices with determinant - 1.
d) All the above.​

Answer 1

Answer:

The final answer

1) b is a subgroup of a

2) b is a subgroup of c

Step-by-step explanation:

Given,

We need to find the subgroups among the given statements.

a) The set of all n * n matrices with determinant 2.

b) The set of all upper triangular n * n matrices with no zeroes on the diagonal.

c) The set of all n * n matrices with determinant -1.

d) All of the above.

The set of all n * n matrices with a determinant ≠ 0 means that the numbers should not have zero between them when they are taken for mulltiplication. This is only possible if the numbers have zero in their diagonal elements. Hence, b is a subgroup of a and c.

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