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**1. Homework Statement**

Show that the matrix [cos(theta), -sin(theta); sin(theta), cos(theta)] is invertible, regardless of the value of theta

**2. Homework Equations**

Identity matrix, elementary row operations

**3. The Attempt at a Solution**

I have the basic idea as to how to go about this; (let the above matrix = A)

- form an augmented matrix with the identity matrix, eg. [A|I]

- perform row operations (forward and backwards elimination) until matrix looks like [I|A^-1]

However, i'm at a loss as to how to perform these operations with the trigonometric values instead of numbers.

Just a push in the right direction would be greatly appreciated, i'd like to solve this myself