Question

If A=[31−24] and B=[03−12] . what is AB?

Answer 1

To find AB, we need to perform matrix multiplication, which involves multiplying the elements of the rows of matrix A by the corresponding elements in the columns of matrix B, and summing them up.

Matrix A: [31 -24]
Matrix B: [03 -12]

The first row of matrix A multiplied by the first column of matrix B:
(3 * 0) + (-2 * 1) = 0 - 2 = -2

The first row of matrix A multiplied by the second column of matrix B:
(3 * 3) + (-2 * -1) = 9 + 2 = 11

The second row of matrix A multiplied by the first column of matrix B:
(-2 * 0) + (4 * 1) = 0 + 4 = 4

The second row of matrix A multiplied by the second column of matrix B:
(-2 * 3) + (4 * -1) = -6 - 4 = -10

Therefore, AB = [-2 11]
[4 -10]