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

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

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.

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

If A = [[1, 2], [3, 4]] and B = [[0, 1], [1, 0]], find AB and BA and state whether they are equal.

Find the projection of a = 2i + 3j + 2k on b = i + 2j + k.