Finding equivalent matrix

[.Celeste.]

My textbook isn't really clear on the method of finding an equivalent matrix. Is there a fixed set of elementary operations to be performed, or is it done purely by trial/error and logic?

Thanks.

[ajb]

By equivalent you mean

 

1) Row or column equivalent? (equal after a finite number of elementary row or column operations ).

 

or

 

2)[math]A \sim B[/math] if [math]B = PAQ[/math] for suitable matrices [math]P,Q[/math]?

 

Either way, there is not going to be a fixed number of elementary operations.