Evaluate:

We need to evaluate the matrix:

Determinant of 2 × 2 matrix is found as,

So,

Using the trigonometric identity,

cos (A + B) = cos A cos B – sin A sin B

Replace A by 15° and B by 75°.

cos (15° + 75°) = cos 15° cos 75° - sin 15° cos 75°

⇒ cos 90° = cos 15° cos 75° - sin 15° cos 75°

So, substituting it, we get

Using the trigonometric identity,

cos 90° = 0

Thus, the value of .