Question

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

Answer 1

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 kA.

It is given that,

kA = 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 0 gives a null matrix.

The product of any matrix by the scalar __0__ is the null matrix.