If P is a 3 3 real matrix such that P^T= aP+(a-1)I , Where a1, then

Question

If P is a 3 3 real matrix such that P^T= aP+(a-1)I , Where a>1, then

Accepted Answer

Correct answer: D. (d) P^T= aP+(a-1)I ⇒P=aP^T+(a-I)I ⇒P^T-P=a(P-P^T) ⇒P=P^T , as a -1 Now, P= aP+(a-1)I ⇒P=-I ⇒ (P )=1 ⇒ ( AdjP )=1

$If P is a 3 \times 3 real matrix such that P^{T} = aP + (a - 1) I, Where a > 1, then$