Question

How do you find AB if `A=((-3, -7, -9), (2, -4, -1), (4, 2, -1))` and `B=((-9, -1, 3), (3, -7, 3), (4, 9, -9))`?

Answer 1

`C=(( -30,-29,51), (-34,17,3 ), (-36,-4,12 ))`

Explanation:

Multiply the rows of A by the columns of B for each entry of the new matric C: `c_(ij) =sum_(k=1)^3 a_(ik)b_(kj)`
`c_11 = a_11b_11 + a_12b_21+a_13b_31 = 18-21-36=-39`
expanding as above we get:
`C=(( -30,-29,51), (-34,17,3 ), (-36,-4,12 ))`