Math Solutions

[Step-by-Step] Suppose that A is an invertible n* n matrix Prove that A^3 is invertible. Prove that if B and C are n* n matrices such that AB=AC, then B=C

Question: Suppose that A is an invertible \(n\times n\) matrix

  1. Prove that \({{A}^{3}}\) is invertible.
  2. Prove that if \(B\) and \(C\) are \(n\times n\) matrices such that \(AB=AC\), then \(B=C\)
  3. If \({{A}^{2}}=A\), find A

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