Square matrix A of order n over R has rank n. Which one of the following statement is not correct?a)AThas rank nb)A has n linearly independent columnsc)A is non — singulard)A is singularCorrect answer is option 'D'. Can you explain this answer?

Question

Square matrix A of order n over R has rank n. Which one of the following statement is not correct?a)AThas rank nb)A has n linearly independent columnsc)A is non &mdash; singulard)A is singularCorrect answer is option 'D'. Can you explain this answer?

Answer

The correct answer is:

c) A is non-singular

If the rank of a square matrix A of order n is equal to n, it means that A is full rank and has n linearly independent rows (or columns). This implies that A is invertible or non-singular. Therefore, statement c) is not correct.

Answer

Since A is of order n and it's rank is given as n which is equal to it's order
we know that A matrix has rank equal to it's order only if it's determinant is equal to some non zero.
so Determinant of A must be non zero
implies that A is non singular
so option C is correct

Answer

It is non singular

Answer

A is singular iff detA is 0

Answer

A square Matrix has rank n it means it has n independent column rank of A is equal to its transpose and detA is not equal to zero hence option D is not correct
option D.

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