Question

If A is a matrix and K is a constant, then \( (KA)^T = K A^T \).

Hint:

A scalar can be factored out of a transpose operation. This is different from the transpose of a product of two matrices, where the order is reversed: \( (AB)^T = B^T A^T \).

Answer 1

Step 1: Recall the properties of the transpose of a matrix. One of the fundamental properties is that for any scalar \( k \) and any matrix \( A \), the transpose of their product is the scalar multiplied by the transpose of the matrix.
Step 2: Applying this property, we have \( (KA)^T = K(A^T) \). The statement is therefore correct.