Evaluate the determinant of [[1, 2, 3], [4, 5, 6], [7, 8, 9]].

Show that the points (1, 2), (3, 6) and (5, 10) are collinear using a determinant.

State the condition on the determinant of the coefficient matrix for a system of linear equations to have a unique solution.

Find the area of the triangle with vertices (1, 2), (4, 6) and (−2, 3) using determinants.

If A is a 3 × 3 matrix with |A| = 5, find |2A| and |adj A|.

Evaluate the integral of x² with respect to x, and the definite integral of x² from 0 to 1.

Find the principal value of sin⁻¹(−1/2) and cos⁻¹(−1/2).