Should AP be equal to the matrix on the right?

If it is left multiplication, that is, PA equals right, obviously there is no answer.

Remember the elementary transformation of matrices.

Follow the method of left row and right column.

That is, the left multiplication is a row transformation and the right multiplication is a column transformation.

Obviously here, the matrix on the right

It consists of the second column of a on the left plus the first column.

Add the third column and the first column to get it.

That is, a is a column transformation, and AP gets the following results.

The original identity matrix e is

1 0 0

0 1 0

0 0 1

The second column is added to the first column and the third column is added to the first column.

What you get is

1 1 1

0 1 0

0 0 1

So choosing the P matrix should be the option of C.