The product of any matrix
Question:

The product of any matrix by the scalar________ is the null matrix.

Solution:

Let $A$ be any matrix and $k$ is any scalar. The matrix obtained by multiplying every element of matrix $A$ by $k$ is called the scalar multiplication of matrix $A$ by $k$. It is denoted by $k A$.

It is given that,

$k A=O$

We know that, a matrix whose all elements are zero is called a null matrix.

Here, $A$ is any matrix. So, when all the element of the matrix $A$ are multiplied by 0 , we will get a matrix whose all elements are zero i.e. a null matrix. Thus, the product of any matrix by the scalar o gives a null matrix.

The product of any matrix by the scalar 0 is the null matrix.