Question

Determine whether the statement below is true or false: If a and adbc, then a is not invertible.

Answer 1

The statement is true. If a and ad < bc, then a is not invertible.

Step-by-step explanation:

The statement is true. In order for a number a to be invertible, it must have a multiplicative inverse. If a is not invertible, it means that there does not exist a number b such that ab = 1. If a and ad < bc, then we can rewrite this inequality as ad - bc < 0. We can then multiply both sides of the inequality by a to get a(ad - bc) < 0. Since a(ad - bc) = a^2d - abc, we have a^2d - abc < 0. We can rearrange this inequality as a^2d < abc, and by dividing both sides by a, we get ad < bc. So if a and ad < bc, then a is not invertible.