If  $$n×n$$ matrix A has only one non-zero element, rank of  A is

Correct option is A

Given:
Matrix A is an n × n square matrix that has only one non-zero element. All other elements are zero.

Solution:

$$A = \begin{bmatrix} 0 & 0 \\ 5 & 0 \end{bmatrix}$$​

The rank of a matrix is the:
"Maximum number of linearly independent rows or columns,"
or
"The order of the largest non-zero minor (i.e., determinant of a square submatrix)."
Since there is only one non-zero element in the matrix, we can select a 1×1 submatrix (i.e., that element itself) which is non-zero.

There is no way to form a 2×2 or higher-order submatrix with a non-zero determinant because the rest of the matrix is filled with zeros.

So, the largest non-zero minor is of order 1.

That means the rank of the matrix is 1.

Final Answer:
A. 1