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# Show without computation that the following determinate is equal to zero?

We are given the matrix:

| 0 2 -3 |

| -2 0 4 |

| 3 -4 0 |

And we are asked to prove that the determinate will be 0, without actually solving for the determinate step-by-step. How do we do this? Thank you! :)

### 2 Answers

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- ElmyrLv 71 decade agoFavorite Answer
Umm...isn't that 24?

d = (aei + bfg + cdh) - (gec + hfa + idb)

aei = 0

bfg = 2 * 4 * 3 = 24

cdh = 0

gec = 0

hfa = 0

idb = 0

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- polki90Lv 41 decade ago
All the entries along the main diagonal are 0. This is a signal that the determinant will be 0. If you want proof, algebraically find the determinant. You will see that the other numbers are multiplied by 0 somewhere.

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