If C = [[1, 2], [3, 5]], find C^2.

If C = [[1, 2], [3, 5]], find C^2.

Step 1: Understand that C^2 means we need to multiply the matrix C by itself.
Step 2: Write down the matrix C: C = [[1, 2], [3, 5]].
Step 3: Set up the multiplication of C by C: C * C = [[1, 2], [3, 5]] * [[1, 2], [3, 5]].
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*5) = 2 + 10 = 12.
Step 6: Calculate the first element of the second row: (3*1 + 5*3) = 3 + 15 = 18.
Step 7: Calculate the second element of the second row: (3*2 + 5*5) = 6 + 25 = 31.
Step 8: Combine all the calculated elements into the resulting matrix: C^2 = [[7, 12], [18, 31]].

Matrix Multiplication – The process of multiplying two matrices by taking the dot product of rows and columns.
Square of a Matrix – Finding the square of a matrix involves multiplying the matrix by itself.