Question

Why can't you square a m≠n matrix?

Option 1: A squared matrix will always have the same dimensions as the original matrix.
Option 2: Squaring a matrix is only possible for square matrices.
Option 3: Squaring a matrix results in a different matrix altogether.
Option 4: The product of the two matrices will not be defined.

Answer 1

You can't square a non-square (m≠n) matrix because matrix multiplication requires the number of columns in the first matrix to equal the number of rows in the second matrix, something that only square matrices can satisfy.

Step-by-step explanation:

The reason you can't square a non-square (m≠n) matrix is because the matrix multiplication operation requires that the number of columns of the first matrix must be equal to the number of rows of the second matrix. When we square a matrix, we are essentially doing matrix multiplication where both matrices involved are the same. Therefore, to square a matrix, it needs to be a square matrix to begin with, meaning the number of rows and columns are equal (m=n).

Now, directly answering the student's question: The correct option is Option 2 - Squaring a matrix is only possible for square matrices. This is because when you try to multiply a non-square matrix by itself, the operation will not be defined since the dimensions will not align as required for matrix multiplication.