Three of these are wrong. Find the one that holds.

Exercise and reference answers

Questions

1. Question

   Three of these statements about A⁻¹ are false.

   Choices

   1. Item

      A⁻¹ = adj A ÷ |A|

      Correct

      Yes

   2. Explanation

      You cannot divide a scalar by a matrix.

      Item

      A⁻¹ = |A| ÷ adj A

   3. Explanation

      The determinant divisor is missing.

      Item

      A⁻¹ = adj A

   4. Explanation

      Only non-singular matrices have one.

      Item

      A⁻¹ exists for every square matrix

2. Question

   Three of these statements about cofactors are false.

   Choices

   1. Item

      Aᵢⱼ = (−1)^(i+j) Mᵢⱼ

      Correct

      Yes

   2. Explanation

      That drops the (−1)^(i+j) sign.

      Item

      Aᵢⱼ = Mᵢⱼ always

   3. Explanation

      The sign alternates with i+j.

      Item

      Aᵢⱼ is always positive

   4. Explanation

      adj A is its TRANSPOSE.

      Item

      adj A is the cofactor matrix itself

Explanation