Question

Let A be a 6 × 5 matrix with entries in ℝ and B be a 5 × 4 matrix with entries in ℝ. Consider the following two statements.
P : For all such nonzero matrices A and B, there is a nonzero matrix Z such that AZB is the 6 × 4 zero matrix.
Q : For all such nonzero matrices A and B, there is a nonzero matrix Y such that BYA is the 5 × 5 zero matrix.
Which one of the following holds ?

• A. Both P and Q are true
• B. P is true but Q is false
• C. P is false but Q is true
• D. Both P and Q are false

Answer 1

Answer: (A)

Both P and Q are true

Answer 2

The correct option is (A) : Both P and Q are true.