For what value of a do the following matrices commute A 2a

For what value of a do the following matrices commute? A = [-2a -2 2 0], B = [1 -2 2 -2]

Solution

for A, and B to commute

AB= BA has to satisfy this condition

AB = [ -2a -4 -4a-4]

[-2 -4 ]

now BA = [1 2] [-2a 2]

[-2 -2] [-2 0]

BA = [-2a-4 2]

[4a+4 -4]

now AB =BA

so 4a +4 =-2

4a = -2-4

4a =-6

a = -3/2

for a=-3/2 A and B are commute