To square a 3×3 matrix, you need to multiply the matrix by itself. This involves using the rules of matrix multiplication. Let’s say we have a matrix A defined as:
A =
| a11 | a12 | a13 |
| a21 | a22 | a23 |
| a31 | a32 | a33 |
To compute the square of this matrix, denoted as A², you perform the following multiplication:
A² = A * A =
| (a11*a11 + a12*a21 + a13*a31) | (a11*a12 + a12*a22 + a13*a32) | (a11*a13 + a12*a23 + a13*a33) |
| (a21*a11 + a22*a21 + a23*a31) | (a21*a12 + a22*a22 + a23*a32) | (a21*a13 + a22*a23 + a23*a33) |
| (a31*a11 + a32*a21 + a33*a31) | (a31*a12 + a32*a22 + a33*a32) | (a31*a13 + a32*a23 + a33*a33) |
Each element of the resulting matrix is calculated by taking the dot product of the corresponding row of the first matrix and the column of the second matrix. Make sure to sum the products accordingly. This process, though it may look complicated, follows a systematic approach and will give you the squared matrix accurately.