<s>[INST] Does the same determinant make two matrices equal to each other? 
Does the same determinant make two matrices equal to each other?

If I have:

Find all values of $x$ that make
$$\begin{pmatrix}2 & -1 &4\\3 & 0 & 5\\4 & 1 & 6\end{pmatrix}=\begin{pmatrix} x & 4\\5 & x\end{pmatrix} $$

Would I calculate and equate the determinants of both matrices to solve this problem?
Edit: Below is the exact question. Do the style of brackets refer to the determinants?

 [/INST] If the problem is about an equality of the determinant, all you have to do is compute the determinants separately. The determinant of the $3\times 3$ matrix is
$$
(2)(0)(6) + (-1)(5)(4) + (4)(3)(1) - (4)(0)(4) - (1)(5)(2) - (6)(3)(-1) = 0 - 20 + 12 - 0 - 10 + 18 = 0.
$$
The $2\times 2$ determinant is just $x^{2} - 20$. Then, we arrive at the equation
$$
0 = x^{2} - 20
$$
which has two possible solutions: $x=\sqrt{20}$ or $x=-\sqrt{20}$. Thus, the answer is (D) if the question refers to determinants.
If not, then there is no solution.
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