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Worksheet: Properties of Inverse Matrices

Q1:

Given that find .

  • A
  • B
  • C
  • D
  • E

Q2:

Consider the shown matrix . Find .

  • A
  • B
  • C
  • D
  • E

Q3:

Consider the shown matrix . Find .

  • A
  • B
  • C
  • D
  • E

Q4:

Consider the shown matrix . Find .

  • A
  • B
  • C
  • D
  • E

Q5:

Consider the shown matrix . Find .

  • A
  • B
  • C
  • D
  • E

Q6:

If 𝐴 is a matrix, which of the following is equal to ο€Ή 𝐴  βˆ’ 1 𝑑 ?

  • A ο€Ή 𝐴  βˆ’ 1 1 𝑑
  • B 𝐴 𝑑
  • C 𝐴 1 𝑑
  • D ο€Ή 𝐴  𝑑 βˆ’ 1
  • E 𝐴 βˆ’ 1

Q7:

Given that determine .

  • A
  • B
  • C
  • D

Q8:

Given that find .

  • A
  • B
  • C
  • D

Q9:

Suppose 𝐴 , 𝐡 , and 𝐢 are invertible 𝑛 Γ— 𝑛 matrices. Which of the following is false?

  • A 𝐴 𝐢 𝐡 βˆ’ 1 is invertible.
  • B ( 𝐴 𝐡 𝐢 ) = 𝐢 𝐡 𝐴 βˆ’ 1 βˆ’ 1 βˆ’ 1 βˆ’ 1
  • C d e t ( 𝐢 𝐴 𝐡 ) β‰  0
  • D 𝐴 𝐡 𝐢 βˆ’ 1 does not have full rank.

Q10:

If 𝐴 is a matrix, which of the following is equal to ο€Ή 𝐴  βˆ’ 1 2 ?

  • A ο€Ή 𝐴  βˆ’ 1 1 2
  • B 𝐴 2
  • C 𝐴 1 2
  • D ο€Ή 𝐴  2 βˆ’ 1

Q11:

If is the identity matrix, which of the following is equal to ?

  • A
  • B
  • C
  • D

Q12:

Given that find .

  • A
  • B
  • C
  • D

Q13:

Given that find .

  • A
  • B
  • C
  • D

Q14:

Given that find .

  • A
  • B
  • C
  • D

Q15:

If 𝐴 and 𝐡 are both nonsingular matrices, then what is the value of ( 𝐴 𝐡 ) βˆ’ 1 ?

  • A 𝐴 𝐡 βˆ’ 1 βˆ’ 1
  • B βˆ’ 𝐴 𝐡
  • C ( 𝐡 𝐴 ) βˆ’ 1
  • D 𝐡 𝐴 βˆ’ 1 βˆ’ 1