Thursday

August 28, 2014

August 28, 2014

Posted by **TP** on Sunday, March 29, 2009 at 2:48am.

The question is "Given some matrix A has the property A*2=A^-1, show that determinant A = 1, i.e |A| = 1"

I've tried for ages, but I can't seem to do it, this is what I got to

A^2= A^-1

|A^2| = |A^-1|

|A|^2 = 1/|A|

Can someone please help?

- Maths - Matrices -
**Count Iblis**, Sunday, March 29, 2009 at 8:17amThe statement isn't true, you have to make additional assumptions. E.g. one could add the condition that all the matrix elements are real. Then |A|^3 =1 and you know that |A| must be a real number, so |A| must be 1.

The condition that the matrix elements are real is sufficient, but not necessary. E.g., take the 2x2 diagonal matrix with exp(2 pi i/3) and

exp(-2 pi i/3) on the diagonal.

**Related Questions**

Math (matrices) - No one answered my matrix question. Let me rephrase: Let A, B...

Math - I have a few questions about T-Matrix. In excel, I am suppose to work ...

math - This is a matrix question. R is the matrix (3r 1) (s 2s) 1. State, in ...

math - This is a matrix question. R is the matrix (3r 1) (s 2s) 1. State, in ...

MATHS----Matrix - For a given square matrix A the predicted values of matrix B ...

Maths: Algebra Matrices Class 12th - matrix{{0, 1, -1}, {2, 1, 3}, {1, 1, 1}} ...

matrices - Two matrices can be multiplied only if their sizes are compatible. ...

algebra-det. - a) Suppose that B is an n กม n matrix, and k is a scalar. Give a ...

Algebra - I have to compute the determinant of the matrix without using a ...

math - Two matrices can be multiplied only if their sizes are compatible. ...