Question

Find all possible 2×2

matrices A that for any 2×2 matrix B, AB = BA.
Hint: AB = BA must hold for all B. Try matrices B that have lots of zero entries.

Answer 1

Explanation:

Consider the following four matrices:

(1000),(0010),(0100),(0001).

See what happens when you solve the equation AB=BA

for each of those four (let B

be each one of those four). To facilitate it, write A=(acbd)

You will get a set of equations for the entries of a

which are easily solved. This trick is quite general.