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)
2x2
2x3
3x2
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.
