a^2=ba

Solution for a^2=ba equation:

Simplifying
a2 = ba

Solving
a2 = ab

Solving for variable 'a'.

Reorder the terms:
-1ab + a2 = ab + -1ab

Combine like terms: ab + -1ab = 0
-1ab + a2 = 0

Factor out the Greatest Common Factor (GCF), 'a'.
a(-1b + a) = 0

Subproblem 1
Set the factor 'a' equal to zero and attempt to solve:

Simplifying
a = 0

Solving
a = 0

Move all terms containing a to the left, all other terms to the right.

Simplifying
a = 0
Subproblem 2
Set the factor '(-1b + a)' equal to zero and attempt to solve:

Simplifying
-1b + a = 0

Reorder the terms:
a + -1b = 0

Solving
a + -1b = 0

Move all terms containing a to the left, all other terms to the right.

Add 'b' to each side of the equation.
a + -1b + b = 0 + b

Combine like terms: -1b + b = 0
a + 0 = 0 + b
a = 0 + b
Remove the zero:
a = b

Simplifying
a = b
Solution
a = {0, b}