Let a and b be n-order matrices, and the following propositions: ①A and b are equivalent; ②A is similar to B; ③ The row vector groups of A and B are equivalent; Have () a.①? ②? ③B。

From the definition of similarity, we can know that "A is similar to B", then there is a reversible matrix P, so that B=P- 1AP.

According to the relationship between elementary transformation and matrix multiplication, we know that

AP is equivalent to performing elementary column transformation on A; P- 1AP is equivalent to elementary row transformation of AP, and the matrices before and after elementary transformation are equivalent.

So a and b are similar? A and b are equivalent, that is, ②? ①

So, A is wrong;

If a and b are equivalent, there is a reversible matrix p, and q makes paq = b.

And the row vector group of A is equivalent to the row vector group of B, then there is a invertible matrix P such that PA = B..

The differences between them are as follows: one is to use the elementary transformation "column transformation"; One is to use only elementary line transformation.

Therefore, if the row vector group of A is equivalent to the row vector group of B, then the matrices A and B are equivalent (at this time Q = E).

But the opposite is not the case.

That is 3? ①

So, B is wrong;

The row vector groups of A and B are equivalent, that is, there is an invertible matrix P such that PA = B..

The conclusion that A and B are similar cannot be drawn (B=P- 1AP).

So, c is wrong;

Therefore, choose: d.