Question

Let A [ 1 2 3 and B [ 1 2 Find AB & BA are they equal? 0 1 4 ] 0 1
2 3 ]

Answer 1

To find AB, we need to multiply A and B in that order. To find BA, we need to multiply B and A in that order.

AB =

1(1) + 2(0) + 3(4) 1(2) + 2(1) + 3(2) 1(0) + 2(1) + 3(3)

0(1) + 1(0) + 4(4) 0(2) + 1(1) + 4(2) 0(0) + 1(1) + 4(3)

which simplifies to

13 10 11

16 9 12

BA =

1(1) + 2(2) + 3(0) 1(0) + 2(1) + 3(1) 1(4) + 2(2) + 3(3)

0(1) + 1(2) + 4(0) 0(0) + 1(1) + 4(1) 0(4) + 1(2) + 4(3)

which simplifies to

5 5 17

2 5 10

Since AB and BA are not equal, we can conclude that matrix multiplication is not commutative in general.

Step-by-step explanation: