Which of the following is correct

see full answer

Start JEE / NEET / Foundation preparation at rupees 99/day !!

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!

An Intiative by Sri Chaitanya

If A and B are square matrices of order 3 such that|A|=−1,|B|=3 ,then the determinant of 3 AB is equal to 27

If A is an invertible matrix, thendet(A−1) is equal todet(A)

If A and B are matrices of the same order ,then(A+B)2=A2+2AB+B2 is possible if:AB=I

None of these

answer is D.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

(a) we have |AB|=|A||B| Also for a square matrix of order3, |KA|=K3|A| because each element of the matrix A is multiplied by k and hence in this case we will have K3 commonSince A is invertible, therefore exists and ∴|3AB|=33|A||B|=27(−1)(3)=−81 (b) Since A is invertible, thereforeA−1 for exists andAA−1=1⇒det(AA−1)=det(I) ⇒det(A)det(A−1)=1⇒det(A−1)=1det(A) (c) (A+B)2=(A+B)(A+B) =A2+AB+BA+B2=A2+2AB+B2 if AB=BA

Watch 3-min video & get full concept clarity

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Books for IIT JEE

Best Books for NEET

Get Expert Academic Guidance – Connect with a Counselor Today!

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Books for IIT JEE

Best Books for NEET