Worksheet: Inverse of a 2x2 Matrix

Practice

In this worksheet, we will practice identifying invertible matrices and finding their inverses.

Q1:

Find the inverse of the following matrix.

  • A
  • B
  • C
  • D
  • E

Q2:

Find the inverse of the following matrix.

  • A
  • B
  • C
  • D
  • E

Q3:

Is the following matrix invertible?

  • Ayes
  • Bno

Q4:

Is the following matrix invertible?

  • Ayes
  • Bno

Q5:

Find the set of real values of 𝑎 for which 𝐴 = 𝑎 2 5 1 𝑎 has a multiplicative inverse.

  • A ℝ
  • B { 5 , − 5 }
  • C ℝ − { 5 }
  • D ℝ − { 5 , − 5 }
  • E ℝ − { 2 5 , 1 }

Q6:

Given that find 𝐴 − 1 .

  • A ⎛ ⎜ ⎜ ⎝ 1 𝑥 0 1 1 𝑦 ⎞ ⎟ ⎟ ⎠ 3 3
  • B ⎛ ⎜ ⎜ ⎝ 1 𝑥 − 1 0 1 𝑦 ⎞ ⎟ ⎟ ⎠ 3 3
  • C ⎛ ⎜ ⎜ ⎝ − 1 𝑥 0 1 − 1 𝑦 ⎞ ⎟ ⎟ ⎠ 3 3
  • D ⎛ ⎜ ⎜ ⎝ 1 𝑥 1 0 1 𝑦 ⎞ ⎟ ⎟ ⎠ 3 3

Q7:

Are the following matrices multiplicative inverses of each other?

  • Ano
  • Byes

Q8:

Find the inverse of the following matrix.

  • A
  • B
  • C
  • D
  • E

Q9:

Find the multiplicative inverse of the matrix 𝐴 = − 4 − 1 0 3 5 , if possible.

  • A 5 1 0 − 3 − 4
  • B 𝐴 has no multiplicative inverse.
  • C 5 − 1 0 3 − 4
  • D ⎛ ⎜ ⎜ ⎝ 1 2 1 − 3 1 0 − 2 5 ⎞ ⎟ ⎟ ⎠
  • E − 4 1 0 − 3 5

Q10:

Given that the following matrix is invertible, what must be true of ?

  • A
  • B
  • C
  • D
  • E

Q11:

Using the elementary row operation, find for the given matrix if possible.

  • A
  • B
  • C
  • D
  • E

Q12:

Find the multiplicative inverse of 𝐴 = − 4 8 − 1 2 2 4 , if possible.

  • A − 1 1 9 2 2 4 − 8 1 2 − 4
  • B − 1 1 9 2 2 4 1 2 − 8 − 4
  • C 2 4 1 2 − 8 − 4
  • D 𝐴 has no multiplicative inverse.

Q13:

Given find its multiplicative inverse if possible.

  • A − 1 3 7 − 4 3 7 4
  • B − 4 7 3 4
  • C 𝐴 has no multiplicative inverse.
  • D − 1 3 7 − 4 7 3 4

Q14:

Find the multiplicative inverse of 6 9 0 0 6 9 .

  • A ⎛ ⎜ ⎜ ⎝ − 1 6 9 0 0 − 1 6 9 ⎞ ⎟ ⎟ ⎠
  • B − 6 9 0 0 − 6 9
  • C 6 9 0 0 − 6 9
  • D ⎛ ⎜ ⎜ ⎝ 1 6 9 0 0 1 6 9 ⎞ ⎟ ⎟ ⎠

Q15:

Given that find the matrix 𝐴 .

  • A − 1 0 5 6 − 2
  • B ⎛ ⎜ ⎜ ⎝ 1 5 1 2 3 5 1 ⎞ ⎟ ⎟ ⎠
  • C − 1 0 − 5 − 6 − 2
  • D ⎛ ⎜ ⎜ ⎝ 1 − 1 2 − 3 5 1 5 ⎞ ⎟ ⎟ ⎠

Q16:

Consider the matrices 𝐴 and 𝐵 . Determine ( 𝐴 + 𝐵 ) 𝐴 = − 3 − 2 − 5 − 7 , 𝐵 = − 1 2 8 9 .

  • A 0 . 5 0 0 . 3 7 5 − 0 . 2 5
  • B − 4 0 3 2
  • C 3 0 − 4 2
  • D − 0 . 2 5 0 0 . 3 7 5 0 . 5

Q17:

Find the multiplicative inverse of

  • A 𝜃 𝜃 𝜃 − 1 t a n s e c s e c 2
  • B 𝜃 𝜃 1 𝜃 s e c t a n s e c 2
  • C 𝜃 − 1 − 𝜃 𝜃 s e c t a n s e c 2
  • D 𝜃 − 𝜃 − 1 𝜃 s e c t a n s e c 2

Q18:

Find the multiplicative inverse of

  • A 𝜃 − 𝜃 𝜃 𝜃 s i n c o s c o s s i n
  • B 𝜃 − 𝜃 𝜃 𝜃 c o s s i n s i n c o s
  • C − 𝜃 𝜃 − 𝜃 − 𝜃 c o s s i n s i n c o s
  • D 𝜃 𝜃 − 𝜃 𝜃 s i n c o s c o s s i n

Q19:

Solve for matrix in the matrix equation , where , , and are as follows.

  • A
  • B
  • C
  • D
  • E

Q20:

Consider the following matrix equation. Solve for the unknown matrix.

  • A
  • B
  • C
  • D
  • E

Q21:

Find the multiplicative inverse of the matrix 𝐴 = 3 7 2 2 , if possible.

  • A 2 − 7 − 2 3
  • B 𝐴 has no multiplicative inverse.
  • C 2 7 2 3
  • D ⎛ ⎜ ⎜ ⎝ − 1 4 7 8 1 4 − 3 8 ⎞ ⎟ ⎟ ⎠
  • E 3 − 7 − 2 2

Q22:

Find the multiplicative inverse of the matrix 𝐴 = 5 − 2 7 − 2 , if possible.

  • A − 2 2 − 7 5
  • B 𝐴 has no multiplicative inverse.
  • C − 2 − 2 7 5
  • D ⎛ ⎜ ⎜ ⎝ − 1 2 1 2 − 7 4 5 4 ⎞ ⎟ ⎟ ⎠
  • E 5 2 − 7 − 2

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