Question

If A = [(1, -1, 1), (-3, 2, -1), (-2, 1, 0)], B = [(1, 2, 3), (2, 4, 6), (1, 2, 3)], then compute AB and BA.

Answer 1

Here, A is 3 × 3 and B is 3 × 3.

Hence, both AB and BA are defined and each will be 3 × 3 matrix. Let

where C_ij means the product of the element at i^th row of A with the element at j^th column of B.

For example, C₂₃ = product of the second row of A with the third column of B. That is,

Similarly, we can find other elements of C.

We can also say that by the product of the first row of A with the three columns of B, we shall get the three elements of the first row of C. That is,

R₁C₁, R₁C₂, R₁C₃

and similarly take the second row of A and multiply with all the columns of B and we will get the three elements of the second row of C, i.e. R₂C₁, R₂C₂, R₂C₃ and elements of the third row of C will be R₃C₁, R₃C₂, R₃C₃. Therefore

Similarly, BA can also be computed.