How do you multiply determinants?
Suppose we have two 2×2 matrices, whose determinants are given by:
∆1=|a1b1a2b2|∆2=|c1d1c2d2|∆1=a1b2-a2b1∆2=c1d2-c2d1
Now multiply ∆1and∆2
∆1∆2=(a1b2-a2b1)(c1d2-c2d1)
A student multiplied 7236 by 65 instead of multiplying by 56. By how much was his answer greater than the correct answer? (Hint: Do you need to do both the multiplications?)