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

If A is a 3x3 matrix and B is a 3x3 matrix, what is the maximum order of the resultant matrix when A is multiplied by B? (2022)

If A is a 3x3 matrix and B is a 3x3 matrix, what is the maximum order of the resultant matrix when A is multiplied by B? (2022)

Step 1: Understand what a matrix is. A matrix is a rectangular array of numbers arranged in rows and columns.
Step 2: Identify the dimensions of the matrices A and B. Both A and B are 3x3 matrices, meaning they have 3 rows and 3 columns.
Step 3: Recall the rule for multiplying matrices. When you multiply two matrices, the number of rows in the first matrix and the number of columns in the second matrix determine the dimensions of the resultant matrix.
Step 4: Since both A and B are 3x3, the multiplication AB is valid because the number of columns in A (3) matches the number of rows in B (3).
Step 5: Determine the dimensions of the resultant matrix. The product AB will have the number of rows from A (3) and the number of columns from B (3).
Step 6: Conclude that the resultant matrix AB is also a 3x3 matrix.

Matrix Multiplication – The order of the resultant matrix from multiplying two matrices is determined by the outer dimensions of the matrices involved.
Matrix Dimensions – Understanding that the dimensions of a matrix are expressed in terms of rows and columns, and that for two matrices to be multiplied, the number of columns in the first must equal the number of rows in the second.