The group of matrices with determinant _________ is a subgroup of the group of invertible matrices under multiplication.
A. 2
B. 3
C. 1
D. 4
Answer:C
The group of matrices with determinant _________ is a subgroup of the group of invertible matrices under multiplication.
A. 2 B. 3 C. 1 D. 4
Explanation: The group of real matrices with determinant 1 is a subgroup of the group of invertible real matrices, both equipped with matrix multiplication. It has to be shown that the product of two matrices with determinant 1 is another matrix with determinant 1, but this is immediate from the multiplicative property of the determinant. This group is usually denoted by(n, R).