If you have the general 3x3 matrix:
the determinant is:
Which further breaks down to:
Note: , and are determinants themselves. If you need help finding the determinant of 2x2 matrices (which is required to find the determinant of 3x3 matrices), check out this solver

From the matrix , we can see that , , , , , , , , and
Start with the general 3x3 determinant.
Plug in the given values (see above)
Multiply
Subtract
Multiply
Combine like terms.
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Answer:
So , which means that the determinant of the matrix is 0
