Question

The rank of a null matrix is
A.0
B.1
C.does not exist
D.none of these

Answer 1

Hint: Here, we have given a null matrix and we should know that a null matrix is a zero matrix. We should also know that the zero matrix has no non-zero rows or columns in the echelon form to find the required value.

Complete step-by-step answer:
We are given that the matrix is a null matrix.
We know that the rank of a matrix refers to the number of linearly independent rows or columns of the matrix.
We also know that the total number of non-zero rows or columns in the row echelon or column echelon form of a matrix defines the maximum number of linearly independent rows or columns of the matrix, where echelon form is when each row containing a non zero number has the number 1 appearing in the rows first non zero columns.
But we are given that the matrix is a null matrix and we know that a null matrix is a zero matrix.
Since the null matrix is a zero matrix, we can use the fact that a zero matrix has no non-zero rows or columns, hence, no independent rows or columns.
So, we have found out that the rank of a null matrix is 0.
Hence, option A is correct.

Note: In solving these types of questions, the key concept of solving is we should have knowledge of how to find the rank of the matrix and meaning of the null matrix. There are many methods to find the rank of certain matrices, which depends on the type of questions.