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If A is a 3x3 matrix and B is a 3x3 matrix, what is the order of the matrix prod

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Question: If A is a 3x3 matrix and B is a 3x3 matrix, what is the order of the matrix product AB? (2021)

Options:

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

Correct Answer: 3x3

Exam Year: 2021

Solution: 

The product of two matrices A and B, both of order 3x3, will also be a matrix of order 3x3.

If A is a 3x3 matrix and B is a 3x3 matrix, what is the order of the matrix prod

Practice Questions

Q1
If A is a 3x3 matrix and B is a 3x3 matrix, what is the order of the matrix product AB? (2021)
  1. 3x3
  2. 2x2
  3. 3x2
  4. 2x3

Questions & Step-by-Step Solutions

If A is a 3x3 matrix and B is a 3x3 matrix, what is the order of the matrix product AB? (2021)
  • Step 1: Identify the order of matrix A. A is a 3x3 matrix.
  • Step 2: Identify the order of matrix B. B is also a 3x3 matrix.
  • Step 3: Understand that when you multiply two matrices, the resulting matrix's order is determined by the orders of the original matrices.
  • Step 4: Since both A and B are 3x3 matrices, the product AB will also be a matrix of order 3x3.
  • Matrix Multiplication – The product of two matrices is defined when the number of columns in the first matrix equals the number of rows in the second matrix. The resulting matrix has dimensions based on the outer dimensions of the two matrices.
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