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If A is a 2x2 matrix and B is a 2x2 matrix, what is the order of the product AB?

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Question: If A is a 2x2 matrix and B is a 2x2 matrix, what is the order of the product AB? (2019)

Options:

  1. 2x2
  2. 2x3
  3. 3x2
  4. 3x3

Correct Answer: 2x2

Exam Year: 2019

Solution: 

The order of the product of two matrices is determined by the outer dimensions. Since both A and B are 2x2 matrices, their product AB will also be a 2x2 matrix.

If A is a 2x2 matrix and B is a 2x2 matrix, what is the order of the product AB?

Practice Questions

Q1
If A is a 2x2 matrix and B is a 2x2 matrix, what is the order of the product AB? (2019)
  1. 2x2
  2. 2x3
  3. 3x2
  4. 3x3

Questions & Step-by-Step Solutions

If A is a 2x2 matrix and B is a 2x2 matrix, what is the order of the product AB? (2019)
  • Step 1: Identify the dimensions of matrix A. Since A is a 2x2 matrix, it has 2 rows and 2 columns.
  • Step 2: Identify the dimensions of matrix B. Since B is also a 2x2 matrix, it also has 2 rows and 2 columns.
  • Step 3: Understand that the product of two matrices is determined by the outer dimensions. The outer dimensions are the number of rows from the first matrix (A) and the number of columns from the second matrix (B).
  • Step 4: Since A has 2 rows and B has 2 columns, the product AB will have 2 rows and 2 columns.
  • Step 5: Conclude that the product AB is a 2x2 matrix.
  • Matrix Multiplication – Understanding that the order of the product of two matrices is determined by their dimensions.
  • Matrix Dimensions – Recognizing that the dimensions of a matrix are given in the form of rows x columns.
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