# Find the determinant of a matrix

#### sara_87

Bonsoir everyone

can anyone confirm if i got the answer right or wrong:

Question:

find the determinant of A. A is a matrix and is equal to

1 5 -3
3 -3 3
2 13 -7

(i think you've already guessed that i don't have latex)

i got -18

I would be grateful if anyone could confirm my answer, and if it's wrong i'll write out all the steps that i did in order to get that answer

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#### Mindscrape

Did you use ninja math or cofactors? I like ninja math:

[(1*-3*-7)+(5*3*2)+(3*13*-3)]-[(-3*-3*2)+(3*13*1)+(5*3*7)]=? <----- Is that -18?

You're correct.

#### turdferguson

According to my TI-83, thats it

#### sara_87

Thank you all so much!...(i knew i was right ;) )

and you could help me further by telling me how to find det(B^3) where det B= 4

i don't think that it's as simple as 4^3...is it?

ninja math?

#### matt grime

Homework Helper
Det is multiplicative (Det(XY)=Det(X)Det(Y)). You have been taught this. So use it.

#### sara_87

so it is 4^3, and my answer is 64

#### Mindscrape

Ninja math, basketweave, whatever you want to call it. You slice along the diagonals. So if you have matrix A, you would do

(A11*A22*A33+A12*A23*A31+A21*A32*A13)-(A13*A22*A31+A12*A21*A33+A23*A32*A11)

Homework Helper
Ninja math, basketweave, whatever you want to call it. You slice along the diagonals. So if you have matrix A, you would do

(A11*A22*A33+A12*A23*A31+A21*A32*A13)-(A13*A22*A31+A12*A21*A33+A23*A32*A11)
That 'Ninja math' method is also called the Sarus rule, and it only applies for determinants of matrices of order 3.

#### Mindscrape

Yes I forgot to mention it is only for 3x3. Sarus rule? I did not know that. I prefer ninja math other Sarus rule though.