3. Find all values of

**a**for which the inverse of the 3 x 3 matrix exists. What is A inverse?

A = (1 1 0

1 0 0

1 2

**a**)

Here is my work

So far I know that if det A is nonzero, then A inverse exists. So I used

A = (1 1 0|1 1

1 0 0|1 0

1 2 a|1 2)

and then I used the shortcut method diagonally. |A| = 1(0)(a)+1(0)(1)+0(1)(2)-0(0)(1)-1(0)(2)-1(1)(a) != 0

So I got -a != 0 so I concluded that a is all real numbers except 0... Is that correct?

Thanks in advance...