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Properties

For all matrices \(A, B\) and scalars \(c, d\), it

• commutes, so

  \(c A = A c\),

• associates, so

  \(c (d A) = (c d) A\),

• distributes over matrix addition, so

  \(c (A + B) = c A + c B\), and

• has exactly one multiplicative identity: \(1\), so

  \(1 A = A\).