anonymous
  • anonymous
Anyone here good with linear algebra?
Mathematics
  • Stacey Warren - Expert brainly.com
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schrodinger
  • schrodinger
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anonymous
  • anonymous
Yes, what's your question?
anonymous
  • anonymous
Suppose A is an nxn matrix, whose determinant is not equal to zero and which satisfies the following condition: A^2=A. Prove that A must be equal to In, where I is the identity matrix. Cite any theorems/ definitions used. It'd be a great help if I could get a little "push" or hint.
anonymous
  • anonymous
Are you taking a college course or middle school? If it's a college course, then you're further ahead than I am.

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anonymous
  • anonymous
Sorry, high school*
anonymous
  • anonymous
Jzzkc, linear algebra isn't the same thing as the algebra of linear equations. :P
anonymous
  • anonymous
College course :(
anonymous
  • anonymous
Det =/= 0 <=> There Exists a nxn matrix B s.t AB = I = BA.
anonymous
  • anonymous
=> A^2 = AA = A => AAB = AB => AI = I => A = I
anonymous
  • anonymous
How did you get A62 = AA to become A?
anonymous
  • anonymous
A^2 = A. The matrix satisfies this condition.
anonymous
  • anonymous
and A^2 = AA.
anonymous
  • anonymous
Are you also famliar with span and null space?
anonymous
  • anonymous
Yes I suppose so.
anonymous
  • anonymous
How did you get from the A^2=AA=A step to the step AAB=AB?
anonymous
  • anonymous
I multiplied B, the matrix that has the property AB = I = AB. The Inverse of A. You could multiply it like this => BAA = BA too if you want.

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