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Learning Goal

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Understand zero and identity matrices

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HSN.VM.C.10
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What you'll learn

  1. Identify the zero matrix $O$ and explain its role as the additive identity for matrix addition.
  2. Construct the identity matrix $I_n$ and verify $AI = IA = A$ for a given square matrix.
  3. Compute the determinant of a $2 \times 2$ matrix using $\det(A) = ad - bc$.
  4. State and apply the theorem: a square matrix has a multiplicative inverse if and only if its determinant is nonzero.
  5. Compute the inverse of an invertible $2 \times 2$ matrix and verify $AA^{-1} = I$.

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1

Zero identity matrices

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