Let M be a `3xx3` matrix satisfying
`{:M[(0),(1),(0)]=[(1),(-1),(6)],M[(1),(-1),(0)]=[(1),(1),(-1)]and","M=[(1),(1),(1)]=[(0),(0),(12)]:}`
Then the sum of the diagonal entries of M, is

Explanation

To solve the problem, we need to find the sum of the diagonal entries of the matrix \( M \) given the conditions provided. Let's denote the elements of the matrix \( M \) as follows:

\[ M = \begin{pmatrix} A & B & C \\ D & E & F \\ G & H & I \end{pmatrix} \]

### Step 1: Use the first condition
From the first condition given:
\[ M \begin{pmatrix} 0 \\ 1 \\ 0 \end{pmatrix} = \begin{pmatrix} 1 \\ -1 \\ 6 \end{pmatrix} \]
This means that when we multiply the first column of \( M \) by the vector \( \begin{pmatrix} 0 \\ 1 \\ 0 \end{pmatrix} \), we get the second column of \( M \):
\[ \begin{pmatrix} B \\ E \\ H \end{pmatrix} = \begin{pmatrix} 1 \\ -1 \\ 6 \end{pmatrix} \]
Thus, we can conclude:
- \( B = 1 \)
- \( E = -1 \)
- \( H = 6 \)

### Step 2: Use the second condition
From the second condition:
\[ M \begin{pmatrix} 1 \\ -1 \\ 0 \end{pmatrix} = \begin{pmatrix} 1 \\ 1 \\ -1 \end{pmatrix} \]
This gives us:
\[ \begin{pmatrix} A - B \\ D - E \\ G - H \end{pmatrix} = \begin{pmatrix} 1 \\ 1 \\ -1 \end{pmatrix} \]
Substituting the known values of \( B \) and \( H \):
- \( A - 1 = 1 \) → \( A = 2 \)
- \( D - (-1) = 1 \) → \( D + 1 = 1 \) → \( D = 0 \)
- \( G - 6 = -1 \) → \( G = 5 \)

### Step 3: Use the third condition
From the third condition:
\[ M \begin{pmatrix} 1 \\ 1 \\ 1 \end{pmatrix} = \begin{pmatrix} 0 \\ 0 \\ 12 \end{pmatrix} \]
This gives us:
\[ \begin{pmatrix} A + B + C \\ D + E + F \\ G + H + I \end{pmatrix} = \begin{pmatrix} 0 \\ 0 \\ 12 \end{pmatrix} \]
Substituting the known values:
1. \( 2 + 1 + C = 0 \) → \( C = -3 \)
2. \( 0 - 1 + F = 0 \) → \( F = 1 \)
3. \( 5 + 6 + I = 12 \) → \( I = 1 \)

### Step 4: Summing the diagonal entries
Now we have all the values:
- \( A = 2 \)
- \( E = -1 \)
- \( I = 1 \)

The sum of the diagonal entries is:
\[ A + E + I = 2 + (-1) + 1 = 2 \]

### Final Answer
The sum of the diagonal entries of matrix \( M \) is \( \boxed{2} \).