Question

Find the products AB and BA to determine whether B is the multiplicative inverse of A. ? a. B ≠ A^-1 b. B = A-1

Answer 1

B is the multiplicative inverse of A and A is the multiplicative inverse of B.

Explanation:

Let's multiply AB first.

First Row, First Column
`5*2+3*(-3)=1`

First Row, Second Column
`5(-3)+3*5=0`

Second Row, First Column
`3*2+2(-3)=0`

Second Row, Second Column
`3(-3)+2*5=1`

So AB = `(1,0)/(0,1)` which is the identity matrix

Lets try BA now.

First Row, First Column
`2*5+3*(-3)=1`

First Row, Second Column
`3*2+2(-3)=0`

Second Row, First Column
`(-5)*3+5*3=0`

Second Row, Second Column
`3(-3)+2*5=1`

So BA = `(1,0)/(0,1)` which is also the identity matrix

A and B are multiplicative inverses.