1,798 views
0 votes
0 votes
Let A be a 4×3 real matrix with rank 2. Let B be transpose matrix of A. Which one of the following statement is TRUE?

(a) Rank of BA is less than 2.

(b) Rank of BA is equal to 2.

(c) Rank of BA is greater than 2.

(d) Rank of BA can be any number between 1 and 3.

1 Answer

2 votes
2 votes
A, B= $A^{T}$

By the property,

Rank(A) = Rank($A^{T}$) = Rank(A$A^{T}$) = Rank($A^{T}$A)

So option is B.

Related questions

3 votes
3 votes
0 answers
2
Parshu gate asked Nov 11, 2017
556 views
The rank of the matrix of coefficients of a homogeneous system of m linear equations in n unknowns is never less than the rank of the augmented matrix.(A) Always true(B) ...
2 votes
2 votes
1 answer
3
harshit agarwal asked Jan 8, 2017
1,640 views
The rank of above matrix is 3 then what is that square sub matrix of order 3 whose determinant is not equal to 0.
4 votes
4 votes
2 answers
4
Nandkishor3939 asked Jan 24, 2019
3,309 views
Nullity of a matrix = Total number columns – Rank of that matrixBut how to calculate value of x when nullity is already given(1 in this case)