Question 1

Prove that the determinant sin cos - sin - 1 cos 1 x x x θ θ θ θ is independent of θ. 2. Evaluate cos cos cos sin - sin - sin cos 0 sin cos sin sin cos α β α β α β β α β α β α . 3. If A-1 = ( ) 3 1 1 1 2 2 15 6 5 and B 1 3 0 , find AB 5 2 2 0 2 1 - - - - - - - -         =           4. Let A = 1 2 1 2 3 1 1 1 5             . Verify that (i) [adj A]-1 = adj (A -1) (ii) (A-1)-1 = A