SOLUTION: Let n ∈ N and B is a n × n matrice with real entries and has determinant 1. Show that there exist n × n matrices K, A and N such that B = KAN.

Question 1183381: Let n ∈ N and B is a n × n matrice with real entries and has determinant 1. Show that there exist n × n matrices
K, A and N such that B = KAN.
Answer by ikleyn(52781) (Show Source): You can put this solution on YOUR website!
.

Surely, for any nxn-matrix B there are nxn-matrices K, A and N such that B = KAN.

Simply take A = B, K = I (the identity matrix), N = I.

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In your post, you missed some important properties of matrices A, B, K and N, that make the problem SPECIAL.

As it is worded in your post, the statement is TRIVIAL.

It is valid for any square nxn-matrix B, independently of its determinant.

So, twice and thrice check with your source.

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The term "matrice" in English is "matrix".

Use "matrix" for single.

Use "matrices" for plural.

Happy learning (!)

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