Is the matrix invertible or not?

Question

Determine whether the following matrix is invertible or not.

Answer 1

1 1 0

1 1 1

0 1 1

----------------

-row1 + row2

1 1 0

0 0 1

0 1 1

----------------------

-row3 + row1

1 0 -1

0 0 1

0 1 1

--------------------------

-row2 + row3

1 0 -1

0 0 1

0 1 0

--------------

row 2 + row1

1 0 0

0 0 1

0 1 0

------------------

swaps rows

1 0 0

0 1 0

0 0 1

yes, it is invertible