Find the inverse of a 3×3 matrix with trigonometric entries

[Reshma]

Find the inverse of A given by:
$$A = \left[\begin{array}{ccc}\cos \phi & -\cos \theta \sin \phi & \sin \theta \sin \phi \\\sin \phi & \cos \theta \cos \phi & -\sin \theta \cos \phi \\0 & \sin \theta & \cos \theta\end{array}\right]$$

I have never encountered a problem in Matrices involving long trigonometric functions. How do I find the inverse? Should I use the same row-reduction method for this?

 

[Data]

Use whatever method you prefer (I like the transposed cofactor matrix method, personally). Once you specify $\theta, \ \phi$, they're just numbers (you should, of course, check to make sure that there are no values of these that stop the matrix from being invertible!).

 

[Reshma]

Ok, thanks a lot! I will try it out.