* | 1 | 2 | 3 | 4 | 5 |
1 | 1 | 1 | 1 | 1 | 1 |
2 | 1 | 2 | 1 | 2 | 1 |
3 | 1 | 1 | 3 | 1 | 1 |
4 | 1 | 2 | 1 | 4 | 1 |
5 | 1 | 1 | 1 | 1 | 5 |
Answer:
(i) (2*3) * 4 = 1 * 4 = 1
and 2 * (3 * 4) = 2 * 1 = 1
Clearly (2 * 3) * 4 = 2 * (3 * 4)
(ii) Since the given composition is symmetrical about the diagonal of multiplication table, therefore* is commutative.
(iii) (2 * 3) * (4 * 5) = 1 * 1 = 1.
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