Step 1: Understand that A^2 means A multiplied by itself, which is A * A.
Step 2: Write down the matrix A: A = [[1, 2], [3, 4]].
Step 3: Set up the multiplication of A by itself: A * A = [[1, 2], [3, 4]] * [[1, 2], [3, 4]].
Step 4: Calculate the first element of the resulting matrix: (1*1 + 2*3) = 1 + 6 = 7.
Step 5: Calculate the second element of the first row: (1*2 + 2*4) = 2 + 8 = 10.
Step 6: Calculate the first element of the second row: (3*1 + 4*3) = 3 + 12 = 15.
Step 7: Calculate the second element of the second row: (3*2 + 4*4) = 6 + 16 = 22.
Step 8: Combine all the calculated elements into the resulting matrix: A^2 = [[7, 10], [15, 22]].
Matrix Multiplication – Understanding how to multiply two matrices, including the rules for dimensions and the calculation of each element in the resulting matrix.
Matrix Squaring – Applying matrix multiplication to a single matrix to find its square, which involves multiplying the matrix by itself.
