-1 = 1??? why not?

right watch this:
SQRT(1)=1
Thus SQRT(1*1)=1
Thus SQRT(-1*-1)=1
theorem: SQRT(a*b)=SQRT(a)*SQRT(b)
Thus SQRT(-1)*SQRT(-1)=1
Theorem: SQRT(-1)=i where i*i=-1 (i for imaginary)
Thus -1=1

Something is wrong. Where?

SQRT(a*b)=SQRT(a)*SQRT(b) only applies when a and b are whole numbers. A whole number is an non-negative and non-zero integer.