__maths__>__Properties of Vector Arithmetics__>__Properties of Cross Product__### Cross Product : No Multiplicative Identity

In this page, learn that the vector cross product does not have multiplicative identity.

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What does 'identical' mean?

- same; similar; alike
- same; similar; alike
- different; mismatch

The answer is 'same; similar; alike'

What is the multiplicative identity in real numbers - number system?

- `1`
- `1`
- `0`
- `-1`

The answer is '`1`'.

For any real number `a`, `a xx 1 = a`, so `1` is the multiplicative identity in real numbers.

Given that `vec p xx vec q` is perpendicular to `vec p` for any `vec q`, is there a vector `vec r` such that `vec p xx vec r = vec p`?

• No multiplicative identity for Cross Product.

**Cross Product does not have a Multiplicative Identity: ** For any vector `vec p in bbb V`, there is no other vector such that cross product between them is `vec p`.

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