Can a Matrix A² ever equal -I₃ in M₃(ℝ)?

AllRelative
Messages
42
Reaction score
2

Homework Statement


Show that no matrix A ∈ M3 (ℝ) exists so that A2 = -I3

Homework Equations

The Attempt at a Solution


This is from a french textbook of first year linear algebra. I'm quite familiar with properties of matrices but I don't have any idea of how to prove this.

Thanks for the help!
 
Physics news on Phys.org
Think about the determinants in the given equation.
 
Compute the determinant of ##A##.
 
I took me a while but I got it. Thanks both of you!
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
View full post »

Similar threads

Hermitian Matrix and Commutation relations
Replies
2
Views
3K
Upper trianglar matrix is a subspace of mxn matrices
Replies
1
Views
2K
Proof regarding determinant of block matrices
Replies
5
Views
5K
Proving a set of matrices is NOT a vector space
Replies
2
Views
3K
Proving Subspace of ℝ^{n} from Linear Algebra Homogeneous System
Replies
8
Views
3K
Showing That the Eigenvalue of a Matrix is 0
Replies
8
Views
2K
Prove that diagonal matrices are symmetric matrices
Replies
1
Views
2K
Prove: (AB)*=A*B* Prove Matrix Conjugate Equality
Replies
7
Views
3K
Matrices and linear transformations. Where did I go wrong?
Replies
2
Views
1K
Proving Two Matrices to be Equal
Replies
5
Views
3K

Hot Threads

Recent Insights

Back
Top