Multiplication in quatenionic algebra should be considered an "operation" for conceptual clarity.(e.g multiplication by iota in the complex plane signifies an anticlockwise rotation by a right angle)

Suppose we have

When the operator i acts on ij the result will be the same as i acting on -ji.That is,

(this is called pre multiplying by i)

Now we know,

Pre multiplying b/s by ij we have

or

(because ij and -ji are the same operators)

This is called post-multiplication by i.

You have pre-multiplied by i on the LHS but post-multiplied on the RHS which has led to this error.