If `[{:(x,2),(18,x):}]=[{:(6,2),(18,6):}]`, then 'x' is equal to `+-6`.

Answer

To solve the equation given by the determinants of the matrices, we start with the matrices:

Matrix 1:
\[ \begin{pmatrix} x & 2 \\ 18 & x \end{pmatrix} \]

Matrix 2:
\[ \begin{pmatrix} 6 & 2 \\ 18 & 6 \end{pmatrix} \]

We need to find the value of \( x \) such that the determinants of both matrices are equal.

### Step 1: Calculate the determinant of Matrix 1
The determinant of a 2x2 matrix
\[ \begin{pmatrix} a & b \\ c & d \end{pmatrix} \]
is given by \( ad - bc \).

For Matrix 1:
\[ \text{Determinant} = x \cdot x - 2 \cdot 18 = x^2 - 36 \]

### Step 2: Calculate the determinant of Matrix 2
For Matrix 2:
\[ \text{Determinant} = 6 \cdot 6 - 2 \cdot 18 = 36 - 36 = 0 \]

### Step 3: Set the determinants equal to each other
Since the determinants of both matrices are equal, we have:
\[ x^2 - 36 = 0 \]

### Step 4: Solve for \( x \)
Rearranging the equation gives:
\[ x^2 = 36 \]
Taking the square root of both sides, we find:
\[ x = \pm 6 \]

### Final Answer
Thus, the value of \( x \) is \( \pm 6 \).

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