Which of the following is correct

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

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)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

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