Homework Help: Help with Cramer's rule

1. Sep 5, 2006

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...

2. Sep 5, 2006

StatusX

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

3. Sep 5, 2006

HallsofIvy

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

4. Sep 6, 2006

Reshma

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

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