Browse Questions

# If $A$ is an invertible matrix and B is a matrix then

$\begin{array}{1 1}(A)\;\text{rank(AB) = rank(A)}\\(B)\;\text{rank(AB) = rank(B)}\\(C)\;\text{rank(AB) > rank(A)}\\(D)\;\text{rank(AB) > rank(B)}\end{array}$

Since A is invertible
$\Rightarrow A^{-1}$ exists
Now rank B=rank $(A^{-1}AB)$
$\qquad\quad\quad\leq$ rank (AB)
But rank (AB) $\leq$ rank B
Hence rank (AB) $\leq$ rank B
Hence (B) is the correct answer.