Lesson: Inverse of a 2x2 Matrix

In this lesson, we will learn how to identify invertible matrices and find their inverses.

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Sample Question Videos

  • 04:01
  • 01:33
  • 02:10

Worksheet: 22 Questions • 17 Videos

Q1:

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

Q2:

Find the inverse of the matrix 𝐴 = 4 2 3 7 .

Q3:

Is the matrix 5 1 1 5 invertible?

Q4:

Is the following matrix invertible? 3 1 3 1

Q5:

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

Q6:

Given that 𝐴 = 𝑥 𝑥 𝑦 0 𝑦 , find 𝐴 .

Q7:

Are the following matrices multiplicative inverses of each other?

Q8:

Find the inverse of the following matrix.

Q9:

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

Q10:

Given that the matrix 7 1 7 𝑎 is invertible, what must be true of 𝑎 .

Q11:

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

Q12:

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

Q13:

Given 𝐴 = 4 7 3 4 , find its multiplicative inverse if possible.

Q14:

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

Q15:

Given that 𝐵 = 2 5 6 1 0 , 𝐴 × 𝐵 = 𝐼 , find the matrix 𝐴 .

Q16:

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

Q17:

Find the multiplicative inverse of 𝜃 𝜃 1 𝜃 . s e c t a n s e c

Q18:

Find the multiplicative inverse of 𝜃 𝜃 𝜃 𝜃 . s i n c o s c o s s i n

Q19:

Solve for matrix 𝑋 in the matrix equation 𝑇 𝑋 + 𝐵 = 𝐶 , where

Q20:

Consider the matrix equation 3 1 0 1 𝑎 𝑏 𝑐 𝑑 + 5 7 1 0 8 = 8 2 2 7 .

Q21:

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

Q22:

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

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