SOLUTION: Given: [2 6 ... [4 -6 ... [2 6 1 3] * -1 3] = 1 3] Is [4 -6 an identity matrix? ...-1 3] (I hope this is not confusing. It is read as (2 6 1 3) in a

Algebra ->  Matrices-and-determiminant -> SOLUTION: Given: [2 6 ... [4 -6 ... [2 6 1 3] * -1 3] = 1 3] Is [4 -6 an identity matrix? ...-1 3] (I hope this is not confusing. It is read as (2 6 1 3) in a      Log On


   

Question 985695: Given:
[2 6 ... [4 -6 ... [2 6
1 3] * -1 3] = 1 3]
Is [4 -6 an identity matrix?
...-1 3]
(I hope this is not confusing. It is read as (2 6 1 3) in a 2x2 matrix times (4 -6 -1 3) in a 2x2 matrix)
Thank you.
Answer by ikleyn(52835) About Me  (Show Source):
You can put this solution on YOUR website!

Your example is

%28matrix%282%2C2%2C+2%2C+6%2C+1%2C+3%29%29x%28matrix%282%2C2%2C+4%2C+-6%2C+-1%2C+3%29%29 = %28matrix%282%2C2%2C+2%2C+6%2C+1%2C+3%29%29,

and your question is:   Does it implies that the matrix   %28matrix%282%2C2%2C+4%2C+-6%2C+-1%2C+3%29%29   is identical?

The answer is  NO.

The matrix %28matrix%282%2C2%2C+4%2C+-6%2C+-1%2C+3%29%29 is not identical.

The operation of multiplication in matrices has different properties than multiplication in real or complex numbers.

In the real domain the equality  a*b = b  does imply  a = 1  (if  b  is not zero).

In the matrix domain it is not so.