Questions: Multiplication of 2 × 2 matrices is commutative.

Transcript text: Multiplication of $2 \times 2$ matrices is commutative.

Solution

Solution Steps

Step 1: Understand the Problem

The problem asks whether the multiplication of $2 \times 2$ matrices is commutative. In mathematics, commutative means that the order of the operation does not affect the result, i.e., $A \times B = B \times A$.

Step 2: Define Commutative Property for Matrices

For matrix multiplication to be commutative, the product of two matrices $A$ and $B$ should be the same regardless of the order: $A \times B = B \times A$.

Step 3: Analyze Matrix Multiplication

Matrix multiplication is generally not commutative. For two $2 \times 2$ matrices $A$ and $B$, the product $A \times B$ is not necessarily equal to $B \times A$. This is because the elements of the resulting matrices depend on the order of multiplication.

Step 4: Conclusion

Since matrix multiplication is not commutative in general, the answer to the question is "never" for $2 \times 2$ matrices.