If A is a 3 × 3 invertible matrix, then what will be the value of k if det(A–1) = (det A)k .

Determine the value of the constant ‘k’ so that the function f(x) =

is continuous at x = 0.

Evaluate :

If a line makes angles 90° and 60° respectively with the positive directions of x and y axes, find the angle which it makes with the positive direction of z-axis.

Show that all the diagonal elements of a skew symmetric matrix are zero.