Lesson Worksheet: Properties of Inverse Matrices Mathematics

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

Q1:

Consider the matrix 𝐴=−31−25. Find 𝐴.

  • A3−12−5
  • B⎡⎢⎢⎣−513113−213313⎤⎥⎥⎦
  • C−52−13
  • D⎡⎢⎢⎣−313213−113513⎤⎥⎥⎦
  • E−31−25

Q2:

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

  • A𝐴
  • B𝐴
  • C𝐴
  • D𝐴

Q3:

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

  • A𝐴𝐵
  • B(𝐵𝐴)
  • C−𝐴𝐵
  • D𝐵𝐴

Q4:

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

  • A𝐴
  • B𝐴
  • C𝐴
  • D𝐴
  • E𝐴

Q5:

Given 𝐴=251321174321218, find 𝐴.

  • A174185111223232
  • B152741132181232
  • C232325111217418
  • D251321174321218
  • E253211132741218

Q6:

Given the matrices 𝐴 and 𝐵 where 𝐴=1−230−14001 and 𝐵=1−250−14001, find 𝐴𝐵.

  • A100010001
  • B1−41001−8001
  • C10001000−1
  • D−1000−1000−1
  • E−14−10010001

Without doing any further calculations, find 𝐴.

  • A−1000−1000−1
  • BMatrix 𝐴 has no inverse.
  • C1−250−14001
  • D100010001
  • E1−230−14001

Q7:

If 𝐴 is a nonsingular square matrix, is it correct that 𝐴⋅𝐴 equals the identity matrix?

  • ANo
  • BYes

Q8:

Given that (𝐴𝐵)=165−3−3321𝐴=−2−1−3−2,, determine 𝐵.

  • A213335
  • B−9−1−3−1
  • C⎡⎢⎢⎣−161612−32⎤⎥⎥⎦
  • D−113−9

Q9:

Given that 𝐴 and 𝐵 are invertible matrices, which of the following is the value of 𝐵⋅(𝐴𝐵)?

  • A𝐴
  • B𝐴
  • C𝐴
  • D𝐵
  • E𝐵

Q10:

Given 𝐴=111517, find 𝐴.

  • A111517
  • B151117
  • C175111
  • D517111
  • E111175

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