Hi. Why does the determinant always equal zero for a matrix of consecutive numbers?

This applies whether the consecutive numbers are in the matrix starting from smallest to largest, or vice versa. It also applies irrespective of whether they are entered row then column or vice versa, which makes sense, I guess.

eg

123

456

789

and

987

654

321

and

147

258

369

all equal 0

If the same group of consecutive numbers are scattered around the matrix however, the determinant will not equal zero.

Oh, and while I have only tested this on a 3x3 matrix, I assume it holds true for any square matrix.

Don't lose any sleep over this one, as I am just asking out of curiousity while trying to get my head around matrix algebra.

Also, does anyone have a GOOD definition of what a determinant actually is?

I understand how it is used in equations, but not what it actually IS.

Thank you.

This applies whether the consecutive numbers are in the matrix starting from smallest to largest, or vice versa. It also applies irrespective of whether they are entered row then column or vice versa, which makes sense, I guess.

eg

123

456

789

and

987

654

321

and

147

258

369

all equal 0

If the same group of consecutive numbers are scattered around the matrix however, the determinant will not equal zero.

Oh, and while I have only tested this on a 3x3 matrix, I assume it holds true for any square matrix.

Don't lose any sleep over this one, as I am just asking out of curiousity while trying to get my head around matrix algebra.

Also, does anyone have a GOOD definition of what a determinant actually is?

I understand how it is used in equations, but not what it actually IS.

Thank you.

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