Question

Which statement correctly describes the relationship between scalar matrices and diagonal matrices?

Options

• Every scalar matrix is a diagonal matrix, but not vice versa.

• Every diagonal matrix is a scalar matrix, but not vice versa.

• A diagonal matrix must be a zero matrix.

• A scalar matrix cannot be a diagonal matrix.

Answer 1

A scalar matrix has zero non-diagonal elements, so it is always a diagonal matrix. A diagonal matrix need not have equal diagonal elements, so it may not be scalar.