Solve for A using Cramer's rule with given k and K | QM problem help

[Reshma]

This is from a QM problem. A & B are the unknowns, k and K are given and $i = \sqrt{-1}$. Use Cramer's rule to find A and show that |A|² = 1.

$$A - B = -1$$
$$ikA - KB = ik$$

I applied Cramer's rule to determine A:

$$A = \frac{\left |\begin{array}{cc} -1 & -1 \\ ik & -K \end{array}\right|}{\left |\begin{array}{cc} 1 & -1 \\ ik & -K \end{array}\right|}$$

So, I am left with:
$$A = \frac{K + ik}{-K + ik}$$

I am stuck here, because this nowhere resembles the result I want to prove. Just guide me...

 

[StatusX]

Whats the problem? That looks correct, and it has magnitude 1.

 

[HallsofIvy]

You might want to put $$A = \frac{K + ik}{-K + ik}$$
in "standard form" by multiplying both numerator and denominator by -K- ik.

 

[Reshma]

Ah, how silly of me . Thanks, HallsofIvy! I got it.