## gjhfdfg 2 years ago Find the products AB and BA to determine whether B is the multiplicative inverse of A.?

1. gjhfdfg

|dw:1360900484563:dw|

2. Hoa

I don't know why we have to find the product of AB and then BA. My work is use Gauss-Jordan method to figure out inverse of A and then compare to B. and |dw:1360901929122:dw| is inverse of A, it is not a multiply matrix of B .

3. gjhfdfg

What do you mean?

This uses the definition of the multiplicative inverse. ie if and only if, \$\$AB=BA=I\$\$ A is the multiplicative inverse of B So find the values of AB and BA and see whether they are equal to identity matrix

5. gjhfdfg

Im lost

6. phi

Find the products AB and BA They want you to practice multiplying 2 matrices. can you multiply A*B ?

7. gjhfdfg

The bottom column of B is suppose to be 0 -1 1, my mistake. But I multiplied a * b & I got, [1 0 0] [0 1 0] [0 0 1]

8. phi

OK, the matrix with 1's on the diagonal is the identity matrix (called I (eye)) a * I will give you a also, if you know a * b = I then you know b is the *inverse* of a you also know b*a= I (but I think they want you to multiply it out and see that it is) and we could just as well say a is the *inverse* of b \[ A^{-1} A = I \] (People use capital letters for matrices (bold face if you can). the use lower case, bold letters for vectors)

9. gjhfdfg

Wouldnt it be B = A^1?

10. phi

you mean "wouldn't it be \[ B = A^{-1} \] the -1 is not an exponent, but means *inverse* You can say that. But the inverse of the inverse \[ (A^{-1})^{-1} = A\] if we take the inverse of both sides \[ B^{-1} = (A^{-1})^{-1} = A \] or \[ A = B^{-1} \] which says A is the inverse of B (or vice versa)

11. gjhfdfg

Ah okay, what would it mean if they "=" had a slash through it?

12. phi

not equal

13. gjhfdfg

Got it, thank you for the help.!