GATE 2005
March 12, 2025GATE 2005
March 12, 2025GATE 2005
| Question 46 |
Consider the set H of all 3 × 3 matrices of the type
|a f e| |0 b d| |0 0 c|
where a, b, c, d, e and f are real numbers and abc ≠ 0. Under the matrix multiplication operation, the set H is
| a group | |
| a monoid but not a group
| |
| a semi group but not a monoid | |
| neither a group nor a semi group
|
Question 46 Explanation:
abc != 0 & Identity matrix is identity then it is non-singular and inverse is also defined.
The algebraic structure is a group because the given matrix can have inverse and the inverse is non-singular.
The algebraic structure is a group because the given matrix can have inverse and the inverse is non-singular.
Correct Answer: A
Question 46 Explanation:
abc != 0 & Identity matrix is identity then it is non-singular and inverse is also defined.
The algebraic structure is a group because the given matrix can have inverse and the inverse is non-singular.
The algebraic structure is a group because the given matrix can have inverse and the inverse is non-singular.