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If A is a 2x2 matrix and B is a 2x3 matrix, what is the order of the product AB?

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Question: If A is a 2x2 matrix and B is a 2x3 matrix, what is the order of the product AB? (2019)

Options:

  1. 2x2
  2. 2x3
  3. 3x2
  4. 2x5

Correct Answer: 2x3

Exam Year: 2019

Solution: 

The order of the product of two matrices is determined by the outer dimensions. Here, A (2x2) and B (2x3) can be multiplied, resulting in a matrix of order 2x3.

If A is a 2x2 matrix and B is a 2x3 matrix, what is the order of the product AB?

Practice Questions

Q1
If A is a 2x2 matrix and B is a 2x3 matrix, what is the order of the product AB? (2019)
  1. 2x2
  2. 2x3
  3. 3x2
  4. 2x5

Questions & Step-by-Step Solutions

If A is a 2x2 matrix and B is a 2x3 matrix, what is the order of the product AB? (2019)
  • Step 1: Identify the dimensions of matrix A. A is a 2x2 matrix, which means it has 2 rows and 2 columns.
  • Step 2: Identify the dimensions of matrix B. B is a 2x3 matrix, which means it has 2 rows and 3 columns.
  • Step 3: Check if the matrices can be multiplied. For two matrices to be multiplied, the number of columns in the first matrix (A) must equal the number of rows in the second matrix (B). Here, A has 2 columns and B has 2 rows, so they can be multiplied.
  • Step 4: Determine the dimensions of the resulting product matrix AB. The number of rows in the product will be the same as the number of rows in A (which is 2), and the number of columns will be the same as the number of columns in B (which is 3).
  • Step 5: Conclude that the order of the product AB is 2x3.
  • Matrix Multiplication – Understanding the rules of matrix multiplication, specifically how the dimensions of the matrices affect the resulting product.
  • Matrix Dimensions – Recognizing the dimensions of matrices and how they relate to the ability to perform multiplication.
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