# Determinate of a matrix

## Homework Statement

From "Introduction to Linear Algebra with applications" by Defranza. Ch.1 section 1.6 prob 30.

Let the matrix

a b c
A = d e f
g h i

Where det(A)= 10

Find

a g d
det b h e
c i f

(sorry I didnt see how to write a matrix in latex, but it should be pretty clear what I mean)

**The matrix looks OK when I am typing it out, but when I submitted the thread it messed with it and it looks really messed up**

Its basically a 3x3 matrix with elements(from a11 to a33) a, b, c, d, e, f, g, h, i

## The Attempt at a Solution

So I noticed that the matrix they are asking to find is the transpose of A, plus the 3rd column has been swapped with the 2nd. I haven't read anything about column swapping, so I am not sure if that would alter the the determinate of a matrix like a row swap would. I know det(Atranspose)=det(A), so I figure the answer to this is either 10 or -10(due to the column swap)

Any advice/hints would be appreciated. I also searched in my book and on google and did not find any conclusive results on column swapping as far as elementary row operations go.

fzero
Homework Helper
Gold Member
What operation on the original matrix corresponds to the column swap on the transpose?

What operation on the original matrix corresponds to the column swap on the transpose?

Ah HA!

so the answer must be -10 correct?

fzero