Bilinear Form is Reflexive iff Symmetric or Alternating

Theorem

Let $\mathbb K$ be a field.

Let $V$ be a vector space over $\mathbb K$.

Let $b$ be a bilinear form on $V$.

Then the following are equivalent:

$(1): \quad$ $b$ is reflexive

$(2): \quad$ $b$ is symmetric or alternating

Proof

1 implies 2

Follows from Reflexive Bilinear Form is Symmetric or Alternating

$\blacksquare$

2 implies 1

Follows from:

Symmetric Bilinear Form is Reflexive

Alternating Bilinear Form is Reflexive

$\blacksquare$