GATE 1995
March 17, 2025GATE 1997
March 18, 2025GATE 1995
| Question 41 |
Let A be the set of all non-singular matrices over real number and let* be the matrix multiplication operation. Then
| A is closed under* but < A, *> is not a semigroup | |
Question 41 Explanation:
As the matrices are non-singular so their determinant ±0. Hence, the inverse matrix always exist. But for a group to be Abelian it should follow commutative property. As matrix multiplication is not commutative, is a group but not an abelian group.
Correct Answer: D
Question 41 Explanation:
As the matrices are non-singular so their determinant ±0. Hence, the inverse matrix always exist. But for a group to be Abelian it should follow commutative property. As matrix multiplication is not commutative, is a group but not an abelian group.