Help with Cramer's rule

Reshma

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

[tex]A - B = -1[/tex]
[tex]ikA - KB = ik[/tex]

I applied Cramer's rule to determine A:

[tex]A = \frac{\left |\begin{array}{cc} -1 & -1 \\ ik & -K \end{array}\right|}{\left |\begin{array}{cc} 1 & -1 \\ ik & -K \end{array}\right|}[/tex]

So, I am left with:
[tex]A = \frac{K + ik}{-K + ik}[/tex]

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 [tex]A = \frac{K + ik}{-K + ik}[/tex]
in "standard form" by multiplying both numerator and denominator by -K- ik.

Reshma

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