Find Determinant of A

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I've tried creating a triangular matrix, tried row reducing but can't figure it out as I keep on having c-unknown in my answer. How would I do this? enter image description here

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Hint:

Expanding along column 1 or row 4 (since they each have two zeros), we arrive at:

$$\det A = -20 - 5 c$$

Can you take it from here?

What part does this determinant play in the inverse of a matrix? Recall that

$$A^{-1} = \dfrac{1}{\det A} adj(A)$$

What does that mean for the value of $c$?