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

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Question: If A is a 3x3 matrix and B is a 3x3 matrix, what is the maximum order of the resultant matrix AB? (2023)

Options:

Correct Answer: 3x3

Exam Year: 2023

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 maximum order of the resultant matrix AB? (2023)

If A is a 3x3 matrix and B is a 3x3 matrix, what is the maximum order of the resultant matrix AB? (2023)

Step 1: Understand what a matrix is. A matrix is a rectangular array of numbers arranged in rows and columns.
Step 2: Identify the order of the matrices A and B. Both A and B are 3x3 matrices, meaning they have 3 rows and 3 columns.
Step 3: Learn about matrix multiplication. 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 multiplication AB will also result in a matrix that has the same number of rows and columns.
Step 5: Conclude that the product AB will also be a 3x3 matrix.

Matrix Multiplication – The product of two matrices of compatible dimensions results in a matrix whose dimensions are determined by the outer dimensions of the multiplied matrices.
Matrix Order – The order of a matrix is defined by the number of rows and columns it contains.