⎛ 0 0 2 ⎞⎛ a b c ⎞ ⎛ 1 0 0 ⎞
⎜0 2 0 ⎟ ⎜d e f ⎟= ⎜0 1 0 ⎟
⎝ 2 0 0 ⎠⎝ g h i ⎠ ⎝ 0 0 1 ⎠
( matrix ) (inverse) (identity)
0×a+0×d+2g=2g=1, so g=½;
Similarly, 2e=1, e=½; 2c=1, c=½ (only 3 elements of the identity are non-zero).
All other elements are zero because all the other elements of the identity matrix are zero.
Therefore the inverse is:
⎛ 0 0 ½ ⎞ ⎛ 0 0 1 ⎞
⎜0 ½ 0 ⎟or ½⎜0 1 0 ⎟
⎝ ½ 0 0 ⎠ ⎝ 1 0 0 ⎠