theorem :: MATRIX_9:46

for K being Field
for a, b, c, d, e, f, g, h, i being Element of K
for M being Matrix of 3,K st M = <*<*a,b,c*>,<*d,e,f*>,<*g,h,i*>*> holds
Det M = ((((((a * e) * i) - ((c * e) * g)) - ((a * f) * h)) + ((b * f) * g)) - ((b * d) * i)) + ((c * d) * h)