Lin. Algebra: Find coordinates on a, b, c, d such that AB=BA

[leo255]

Homework Statement

[/B]
Matrix A =

1 1
0 1

Matrix B =

a b
c d

Find coordinates on a, b, c, d such that AB = BA.

Homework Equations

The Attempt at a Solution

I calculated AB and BA with simple matrix multiplication, but am not sure where to go from here.

AB =

a + c a + b
c | d

BA =

a | a + b
c | c + d

 

[Mark44]

Homework Statement

[/B]
Matrix A =

1 1
0 1

Matrix B =

a b
c d

Find coordinates on a, b, c, d such that AB = BA.

Homework Equations

The Attempt at a Solution

I calculated AB and BA with simple matrix multiplication, but am not sure where to go from here.

AB =

a + c a + b
c | d

BA =

a | a + b
c | c + d

Assuming your work so far is correct (I didn't check), set the elements of AB equal to those of BA. This will give you four equations in your four variables.