Brahmagupta Identity

Let

$$\beta\equiv \vert B\vert=x^2-ty^2,$$

where $B$ is the Brahmagupta Matrix, then

$$\mathop{\rm det} [B(x_1,y_1)B(x_2,y_2)] = \mathop{\rm det}[B(x_1,y_1)]\mathop{\rm det}[B(x_2,y_2)]$$

$$= \beta_1\beta_2.$$

References

Suryanarayan, E. R. ``The Brahmagupta Polynomials.'' Fib. Quart. 34, 30-39, 1996.