Lesson Worksheet: Properties of Inverse Matrices Mathematics

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


Consider the matrix 𝐴=3125. Find 𝐴.

  • A3125
  • B513113213313
  • C5213
  • D313213113513
  • E3125


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

  • A𝐴
  • B𝐴
  • C𝐴
  • D𝐴


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

  • A𝐴𝐵
  • B(𝐵𝐴)
  • C𝐴𝐵
  • D𝐵𝐴


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

  • A𝐴
  • B𝐴
  • C𝐴
  • D𝐴
  • E𝐴


Given 𝐴=251321174321218, find 𝐴.

  • A174185111223232
  • B152741132181232
  • C232325111217418
  • D251321174321218
  • E253211132741218


Given the matrices 𝐴 and 𝐵 where 𝐴=123014001 and 𝐵=125014001, find 𝐴𝐵.

  • A100010001
  • B1410018001
  • C100010001
  • D100010001
  • E1410010001

Without doing any further calculations, find 𝐴.

  • A100010001
  • BMatrix 𝐴 has no inverse.
  • C125014001
  • D100010001
  • E123014001


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

  • ANo
  • BYes


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

  • A213335
  • B9131
  • C16161232
  • D1139


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

  • A𝐴
  • B𝐴
  • C𝐴
  • D𝐵
  • E𝐵


Given 𝐴=111517, find 𝐴.

  • A111517
  • B151117
  • C175111
  • D517111
  • E111175

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