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The group of matrices with determinant _________ is a subgroup of the group of invertible matrices under multiplication.

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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

This question was addressed to me by my college director while I was bunking the class.

My question is from Groups topic in portion Groups of Discrete Mathematics

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Right choice is (c) 1

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).

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