Problem 81 - Algebra and Trigonometry

Question

Find two matrices \(A\) and \(B\) such that \(A B=B A\)

Step-by-Step Solution

Answer

The matrices \(A = [2]\) and \(B = [3]\) satisfy the condition \(A B=B A\). Both products \(A B\) and \(B A\) are equal to [6].

Step 1: Define the matrices

Let's define two 1x1 matrices. The 1x1 matrix is essentially a scalar value.\n\nThus, let \(A = [2]\) and \(B = [3]\)

Step 2: Compute the products

Matrix multiplication for 1x1 matrices is simply scalar multiplication. By computing \(A B\) and \(B A\), one would obtain:\n\n\(A B = [2] * [3] = [6]\)\n\(B A = [3] * [2] = [6]\)

Step 3: Verify the result

Clearly, \(A B = B A = [6]\). Thus, the defined matrices satisfy the given condition.