Find the maximum value of .

We need to find the maximum value of

Let us find the determinant,

Determinant of 3 × 3 matrices is found as,

So,

Multiply and divide by 2 on right hand side,

[∵, By trigonometric identity, sin 2θ = 2 sin θ cos θ]

We need to find the maximum value of .

We know the range of sine function.

-1 ≤ sin A ≤ 1

Or,

-1 ≤ sin 2θ ≤ 1

∴, maximum value of sin 2θ is 1.

⇒ maximum value of = 1/2

Thus, maximum value of