Question

If for a matrix, rank equals both the number of rows and number of columns, then the matrix is called

• A. non-singular
• B. singular
• C. transpose
• D. minor

Answer 1

The correct option is A non-singular

Given that both rows and columns are equal. So let us consider $A_{n\times n}$

Also given that $\rho \left(A\right)$ = number of rows of A = number of column of A.

So $\rho \left(A\right)=n$

$\Rightarrow \left|A\right|\ne 0$
Hence A is non-singular