How do I show that these determinants of matrices are equal?

to the 2nd determinant do the following operations and automatically the answer will come out


r1-> - r1
c4-> - c4
r2-> - r2
c3-> - c3

since it done 4 times all the negatives will get cancelled out

sorry i was in a bit of hurry cudnt write the determinant in every step

hope it helps

The theory underlying determinant is this:  There are 3 elementary row operations: 1. row interchange; 2. multiply a row by a constant; and 3. replace a row with combination of the other rows.

The determinant of row operation #2 (multiply a row by a constant r) is = to multiplying the determinant by r.

Since the second matrix involves multiplying 4 rows by -1, then four elementary row operations (#2) are performed.  The resulting determinant = (-1)^4 = 1.  So the determinant of the second matrix = (-1)^4 * determinant of the first.