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Singular or non-singular?

Exercise and reference answers

Items
  1. Item
    |A| = 0
    Category
    Singular
  2. Item
    |A| = −7
    Category
    Non-singular
  3. Item
    A has no inverse
    Category
    Singular
  4. Item
    A⁻¹ exists
    Category
    Non-singular
  5. Item
    |A| = 1
    Category
    Non-singular
  6. Item
    A(adj A) = O
    Category
    Singular
Categories
  1. Item
    Singular
  2. Item
    Non-singular

Explanation

Your syllabus defines a square matrix as singular when |A| = 0 and non-singular when |A| ≠ 0. The whole inverse story hangs on which side a matrix falls. Source: syllabus Maths Part I, Ch 4 Determinants.
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