@Directrix Find the products AB and BA to determine whether B is the multiplicative inverse of A.

A = , B =
A. B = A-1

B. B ≠ A-1

Question

@Directrix   Find the products AB and BA to determine whether B is the multiplicative inverse of A.

A = , B =
	A. B = A-1
	
	B. B ≠ A-1

yacoub1993 · Answer

Is B correct

directrix · Answer

Let me crank it out and see what I get.

yacoub1993 · Answer

ok

directrix · Answer

For A x B, I'm seeing   1 0
                                   0 1

For B x A, I'm seeing    1 0
                                    0 1

directrix · Answer

So, how do we interpret that?

yacoub1993 · Answer

it means that they r equal

directrix · Answer

Those two products are identical but the two matrices A and B are not the same.  

Agree?

yacoub1993 · Answer

yes i agree the two matrices A and B are not the same

directrix · Answer

Do you still think this answer option is correct: >>> Is B correct

yacoub1993 · Answer

no they are equal, its A

directrix · Answer

In words, this "A.   B = A-1" means that matrix B is the inverse of matrix A.

When you multiply a Matrix by its Inverse you get the Identity Matrix (which is like "1" for Matrices).

1 0
0 1        is the identity matrix for 2 x 2 matrices.

directrix · Answer

So, yes,  A)  A. B = A-1 because of the above logic.

directrix · Answer

You can read more about this here: http://www.mathsisfun.com/algebra/matrix-inverse.html