Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.

Start Practicing

Worksheet: Inverse of a 2x2 Matrix

Q1:

Find the inverse of the matrix 𝐴 =  3 3 1 6  .

  • A 𝐴 = 1 1 5  βˆ’ 3 1 3 βˆ’ 6  βˆ’ 1
  • B 𝐴 = 1 2 1  6 βˆ’ 3 βˆ’ 1 3  βˆ’ 1
  • C 𝐴 = 1 2 1  βˆ’ 3 1 3 βˆ’ 6  βˆ’ 1
  • D 𝐴 = 1 1 5  6 βˆ’ 3 βˆ’ 1 3  βˆ’ 1
  • E 𝐴 = 1 1 5  6 3 1 3  βˆ’ 1

Q2:

Find the set of real values of for which has a multiplicative inverse.

  • A
  • B
  • C
  • D
  • E

Q3:

Given that find .

  • A
  • B
  • C
  • D

Q4:

Find the multiplicative inverse of

  • A
  • B
  • C
  • D

Q5:

Given that find the matrix .

  • A
  • B
  • C
  • D

Q6:

Is the following matrix invertible?

  • Ayes
  • Bno

Q7:

Find the multiplicative inverse of the following matrix if possible.

  • A βˆ’ 1 1 9 2  2 4 βˆ’ 8 1 2 βˆ’ 4 
  • B βˆ’ 1 1 9 2  2 4 1 2 βˆ’ 8 βˆ’ 4 
  • C  2 4 1 2 βˆ’ 8 βˆ’ 4 
  • D 𝐴 has no multiplicative inverse.

Q8:

Using the elementary row operation, find 𝐴 βˆ’ 1 for the matrix 𝐴 =  5 3 2 1  if possible.

  • A 𝐴 =  βˆ’ 1 3 2 5  βˆ’ 1
  • B 𝐴 =  1 3 2 5  βˆ’ 1
  • C 𝐴 =  3 βˆ’ 1 βˆ’ 5 2  βˆ’ 1
  • D 𝐴 =  βˆ’ 1 3 2 βˆ’ 5  βˆ’ 1
  • E 𝐴 =  3 1 5 2  βˆ’ 1

Q9:

Given find its multiplicative inverse if possible.

  • A
  • B
  • C has no multiplicative inverse.
  • D

Q10:

Solve for matrix 𝑋 in the matrix equation 𝑇 𝑋 + 𝐡 = 𝐢 , where

  • A  βˆ’ 1 3 βˆ’ 4 βˆ’ 5 
  • B  3 βˆ’ 9 1 2 1 5 
  • C  0 βˆ’ 1 2 βˆ’ 1 1 βˆ’ 4 
  • D  1 βˆ’ 3 4 5 
  • E  6 βˆ’ 6 1 5 1 8 

Q11:

Find the multiplicative inverse of .

  • A
  • B
  • C
  • D

Q12:

Find the multiplicative inverse of the matrix , if possible.

  • A
  • B has no multiplicative inverse.
  • C
  • D
  • E

Q13:

Find the multiplicative inverse of the matrix , if possible.

  • A
  • B has no multiplicative inverse.
  • C
  • D
  • E

Q14:

Find the multiplicative inverse of the matrix , if possible.

  • A
  • B has no multiplicative inverse.
  • C
  • D
  • E

Q15:

Are the following matrices multiplicative inverses of each other?

  • Ano
  • Byes

Q16:

Consider the matrices and . Determine

  • A
  • B
  • C
  • D

Q17:

Given that the matrix  7 1 βˆ’ 7 π‘Ž  is invertible, what must be true of π‘Ž .

  • A π‘Ž β‰  βˆ’ 7
  • B π‘Ž β‰  1
  • C π‘Ž β‰  7
  • D π‘Ž β‰  βˆ’ 1
  • E π‘Ž β‰  0

Q18:

Find the multiplicative inverse of

  • A
  • B
  • C
  • D

Q19:

Find the inverse of the matrix 𝐴 =  4 βˆ’ 2 3 7  .

  • A 𝐴 = 1 2 2  βˆ’ 4 3 βˆ’ 2 βˆ’ 7  βˆ’ 1
  • B 𝐴 = 1 2 2  7 2 βˆ’ 3 4  βˆ’ 1
  • C 𝐴 = 1 3 4  βˆ’ 4 3 βˆ’ 2 βˆ’ 7  βˆ’ 1
  • D 𝐴 = 1 3 4  7 2 βˆ’ 3 4  βˆ’ 1
  • E 𝐴 = 1 3 4  7 βˆ’ 2 3 4  βˆ’ 1

Q20:

Consider the matrix equation

  • A  βˆ’ 1 βˆ’ 9 βˆ’ 1 2 βˆ’ 1 5 
  • B  3 βˆ’ 9 1 2 1 5 
  • C  1 βˆ’ 3 4 5 
  • D  βˆ’ 3 βˆ’ 8 1 2 1 5 
  • E  βˆ’ 3 8 4 5 

Q21:

Is the matrix  5 1 βˆ’ 1 5  invertible?

  • AYes
  • BNo

Q22:

Find the inverse of the following matrix.

  • A 𝐴 = 1 9  8 βˆ’ 1 1 βˆ’ 1  βˆ’ 1
  • B 𝐴 = 1 7  8 βˆ’ 1 1 βˆ’ 1  βˆ’ 1
  • C 𝐴 = 1 9  βˆ’ 8 1 βˆ’ 1 1  βˆ’ 1
  • D 𝐴 = 1 7  βˆ’ 8 1 βˆ’ 1 1  βˆ’ 1
  • E 𝐴 = 1 9  βˆ’ 8 βˆ’ 1 βˆ’ 1 βˆ’ 1  βˆ’ 1