Let A be a scalar matrix of order 3 whose diagonal elements are all equal to 4. If B is any square matrix of order 3, then AB is equal to
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 4B
A scalar matrix is a diagonal matrix with all diagonal elements equal. So
\( \displaystyle A = \begin{bmatrix}4&0&0\\0&4&0\\0&0&4\end{bmatrix} = 4I \)
where I is the identity matrix of order 3. Since \(IB = B\),
\(AB = (4I)B = 4(IB) = 4B\)
So multiplying by A simply multiplies every element of B by 4.