GATE 2021 | MATHS | Q-11

Question

Let $ \mathbf{A} $ be a $ 3 \times 4 $ matrix and $ \mathbf{B} $ be a $ 4 \times 3 $ matrix with real entries such that $ \mathbf{A}\mathbf{B} $ is non-singular. Consider the following statements:

    $P:$ Nullity of $ \mathbf{A} $ is $ 0 $.
    $Q:$ $ \mathbf{B}\mathbf{A} $ is a non-singular matrix.

Then

(A)]both P and Q are TRUE

(B) P is TRUE and Q is FALSE

(C) P is FALSE and Q is TRUE

(D) both P and Q are FALSE