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Lesson Worksheet: Properties of Matrix Multiplication Mathematics • 10th Grade

In this worksheet, we will practice identifying the properties of matrix multiplication, including the transpose of the product of two matrices, and comparing them to the properties of multiplication of numbers.


Which of the following satisfies the equation 𝑋5βˆ’41βˆ’454=5βˆ’41βˆ’454?

  • A𝑋=100010001
  • B𝑋=1111
  • C𝑋=111111111
  • D𝑋=1001


Given three matrices 𝐴,𝐡, and 𝐢, which of the following is equivalent to 𝐴(𝐡+𝐢)?

  • A𝐡𝐴+𝐢𝐴
  • B𝐴𝐡+𝐢
  • C𝐡+𝐴𝐢
  • D𝐡𝐴+𝐢
  • E𝐴𝐡+𝐴𝐢


Given that 𝐴=ο”βˆ’422βˆ’4,𝐡=ο”βˆ’3βˆ’3βˆ’11, find 𝐴𝐡 and 𝐡𝐴.

  • A𝐴𝐡=1014βˆ’2βˆ’10, 𝐡𝐴=666βˆ’6
  • B𝐴𝐡=10βˆ’214βˆ’10, 𝐡𝐴=666βˆ’6
  • C𝐴𝐡=1014βˆ’2βˆ’10, 𝐡𝐴=1014βˆ’2βˆ’10
  • D𝐴𝐡=666βˆ’6, 𝐡𝐴=666βˆ’6


Consider the 2Γ—2 matrices 𝐴=1100 and 𝐡=0101. Is 𝐴𝐡=𝐡𝐴?

  • ANo
  • BYes


Given that 𝐴=ο”βˆ’14βˆ’111 and 𝐼 is the identity matrix of the same order as 𝐴, find 𝐴×𝐼 and 𝐼.

  • A𝐴×𝐼=𝐴, 𝐼=𝐼
  • B𝐴×𝐼=𝐴, 𝐼=π‘›πΌοŠ¨
  • C𝐴×𝐼=𝐴, 𝐼=π‘›πΌοŠ¨
  • D𝐴×𝐼=𝐴, 𝐼=𝐼


Suppose that 𝐴=1βˆ’3βˆ’42, 𝐡=201βˆ’1, and 𝐢=01βˆ’30.

Find 𝐴𝐡.

  • A2βˆ’65βˆ’5
  • Bο”βˆ’42βˆ’39
  • C3βˆ’3βˆ’31
  • Dο”βˆ’13βˆ’6βˆ’2
  • E91βˆ’6βˆ’4

Find 𝐴𝐢.

  • Aο”βˆ’13βˆ’6βˆ’2
  • B3βˆ’3βˆ’31
  • C91βˆ’6βˆ’4
  • D1βˆ’2βˆ’72
  • E2βˆ’65βˆ’5

Find 𝐴(2𝐡+7𝐢).

  • Aο”βˆ’242βˆ’1153
  • Bο”βˆ’2βˆ’424
  • C84βˆ’12βˆ’6
  • D6113βˆ’54βˆ’32
  • Eο”βˆ’213βˆ’33βˆ’4

Express 𝐴(2𝐡+7𝐢) in terms of 𝐴𝐡 and 𝐴𝐢.

  • A2𝐡𝐴+7𝐢𝐴
  • B2𝐴𝐡+7𝐴𝐢
  • C2𝐴𝐡+7𝐢
  • D2𝐡+7𝐴𝐢
  • E2𝐡𝐴+7𝐢


Given that 𝐴=03βˆ’216βˆ’1,𝐡=ο”βˆ’5βˆ’614,𝐢=ο”βˆ’304βˆ’2, is it true that (𝐴𝐡)𝐢=𝐴(𝐡𝐢)?

  • ANo
  • BYes


Let 𝐴=1βˆ’230,𝐡=ο”βˆ’1022, and 𝐢=ο”βˆ’2104.

Find 𝐴𝐡.

  • Aο”βˆ’5βˆ’4βˆ’30
  • Bο”βˆ’5430
  • C54βˆ’30
  • Dο”βˆ’128βˆ’4
  • E1284

Find (𝐴𝐡)𝐢.

  • A0βˆ’8βˆ’1013
  • B3βˆ’3βˆ’110
  • C33βˆ’110
  • D102163
  • E10βˆ’216βˆ’3

Find 𝐡𝐢.

  • A21410
  • B2βˆ’1βˆ’410
  • C4588
  • D4βˆ’2βˆ’88
  • E4288

Find 𝐴(𝐡𝐢).

  • A102163
  • B7334
  • Cο”βˆ’7βˆ’3βˆ’34
  • D10βˆ’216βˆ’3
  • E0βˆ’8βˆ’1013


True or False: If 𝐴 and 𝐡 are both 2Γ—2 matrices, then 𝐴𝐡 is never the same as 𝐡𝐴.

  • AFalse
  • BTrue


Given that 𝐡𝐴=8βˆ’4βˆ’7βˆ’5, what is 𝐴𝐡?

  • A8βˆ’4βˆ’7βˆ’5
  • B8βˆ’7βˆ’4βˆ’5
  • Cο”βˆ’5βˆ’4βˆ’78
  • Dο”βˆ’5βˆ’7βˆ’48

This lesson includes 26 additional questions and 80 additional question variations for subscribers.

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