Simplify the Matrix [[2,2,2],[4,4,4]]^2

Problem

[[2,2,2],[4,4,4]]2

Solution

1. Identify the dimensions of the given matrix. The matrix has 2 rows and 3 columns, making it a 2×3 matrix.

2. Apply the rule for matrix multiplication. To square a matrix A the operation A×A must be performed.

3. Check for compatibility of the dimensions. For the product A×A to be defined, the number of columns in the first matrix must equal the number of rows in the second matrix.

4. Determine if the operation is possible. Since the number of columns (3) does not equal the number of rows (2), the multiplication is undefined.

Final Answer

[[2,2,2],[4,4,4]]2=Undefined

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