Worksheet: Properties of Inverse Matrices

In this worksheet, we will practice using some properties of matrix inverse.

Q1:

If 𝐴 is a matrix, which of the following is equal to 𝐴?

  • A 𝐴
  • B 𝐴
  • C 𝐴
  • D 𝐴

Q2:

Consider the matrix 𝐴=3125. Find 𝐴.

  • A 3 1 2 5
  • B 5 1 3 1 1 3 2 1 3 3 1 3
  • C 5 2 1 3
  • D 3 1 3 2 1 3 1 1 3 5 1 3
  • E 3 1 2 5

Q3:

If 𝐴 and 𝐵 are both nonsingular matrices, then what is the value of (𝐴𝐵)?

  • A 𝐴 𝐵
  • B ( 𝐵 𝐴 )
  • C 𝐴 𝐵
  • D 𝐵 𝐴

Q4:

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

  • A 0 1 1 0
  • B 𝐼
  • C 1 1 1 1
  • D 𝐼

Q5:

Given that 𝐴=6213, find 𝐴.

  • A 6 2 1 3
  • B 3 1 2 6
  • C 3 1 2 6
  • D 6 2 1 3

Q6:

Given that (𝐴𝐵)=16533321𝐴=2132,, determine 𝐵.

  • A 2 1 3 3 3 5
  • B 9 1 3 1
  • C 1 6 1 6 1 2 3 2
  • D 1 1 3 9

Q7:

Given that 𝐴=5265𝐵=2242,, find 𝐵𝐴.

  • A 9 2 6 7 2 6 8 1 3 1 1 2 6
  • B 1 1 2 6 7 2 6 8 1 3 9 2 6
  • C 9 2 6 7 2 6 8 1 3 1 1 2 6
  • D 1 1 2 6 7 2 6 8 1 3 9 2 6

Q8:

If 𝐴 is a matrix, which of the following is equal to 𝐴?

  • A 𝐴
  • B 𝐴
  • C 𝐴
  • D 𝐴
  • E 𝐴

Q9:

Consider the matrix 𝐴=6120. Find 𝐴.

  • A 6 1 2 0
  • B 0 1 2 1 3
  • C 0 2 1 6
  • D 3 1 1 2 0
  • E 6 1 2 0

Q10:

Consider the matrix 𝐴=5462. Find 𝐴.

  • A 5 4 6 2
  • B 1 7 2 7 3 7 5 1 4
  • C 2 6 4 5
  • D 5 1 4 3 7 2 7 1 7
  • E 5 4 6 2

Q11:

Consider the matrix 𝐴=5132. Find 𝐴.

  • A 5 1 3 2
  • B 2 1 3 1 1 3 3 1 3 5 1 3
  • C 2 3 1 5
  • D 5 1 3 3 1 3 1 1 3 2 1 3
  • E 5 1 3 2

Q12:

Given that 𝐴=7216, find 𝐴.

  • A 7 2 1 6
  • B 6 1 2 7
  • C 6 1 2 7
  • D 7 2 1 6

Q13:

Given that 𝐴=2541, find 𝐴.

  • A 2 5 4 1
  • B 1 4 5 2
  • C 1 4 5 2
  • D 2 5 4 1

Q14:

Determine whether the following statement is true or false: If 𝐴 exists, then detdet𝐴=(𝐴).

  • Atrue
  • Bfalse

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