Two are true, one is not

Exercise and reference answers

Questions

1. False statement

   A minor is found by deleting two rows

   Statements

   1. A minor is found by deleting two rows
   2. Cofactor Aᵢⱼ = (−1)^(i+j) Mᵢⱼ
   3. adj A is the transpose of the cofactor matrix

2. False statement

   Every square matrix is invertible

   Statements

   1. A is singular when |A| = 0
   2. Every square matrix is invertible
   3. A (adj A) = |A| I

3. False statement

   |A| changes if you expand along a different row

   Statements

   1. Expansion is easiest along the row with most zeros
   2. A determinant may be expanded along any column
   3. |A| changes if you expand along a different row

Explanation