Question

If k is scalar $(k\ne 0)$, I is an identity matrix and A is a square matrix . Then which among the following will always be a scalar matrix.

• A. $kA$
• B. $kI$
• C. $\frac{1}{k}.A$
• D. $\frac{1}{k}.I$

Answer 1

Answer: (B), (D)

$\frac{1}{k}.I$

If k is a scalar, then $\frac{1}{k}$ is also a scalar since k≠0. You might remember that a scalar can be any real number. And it cannot be an indeterminate value or infinity. You get a scalar matrix when a scalar is multiplied with an identity matrix which is true for the options (b) and (d).