Answer:
b. BC
Step-by-step explanation:
The first thing is to calculate the dimensions of each matrix, that is, the number of rows x number of columns:
dimensions of A: 2x2
B dimensions: 2x3
C dimensions: 3x3
D dimensions: 1x3
We have that a matrix multiplication is defined, the internal numbers of its dimensions must be the same: we analyze each option:
BA: (2x3) * (2x2): the internal numbers do not match (a 3 for B and a 2 for A), so the multiplication of the matrix is not defined
BC: (2x3) * (3x3): the internal numbers are both 3, so the matrix multiplication is defined
CB: (3x3
) * (2x3): the internal numbers do not match (a 3 for C and a 2 for B), so the multiplication of the matrix is not defined
CD: (3x3) * (1x3): the internal numbers do not match (a 3 for C and a 1 for D) so the multiplication of the matrix is not defined
Therefore the answer is b. BC
