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

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1 Answer
Apr 21, 2018

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.