Q.

Let M be a 3×3 invertible matrix with real entries and let I denote the 3×3 identity matrix. If M−1= adj (adj M), then which of the following statement is/are ALWAYS TRUE ?

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

a

M=I

b

det M=1

c

M2=I

d

(adj⁡M)2=I

answer is B.

(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

det⁡(M)≠0M−1=adj⁡(adj⁡M)M−1=det⁡(M)⋅M     since adjadj A=An-2AM−1M=det⁡(M)⋅M2I=det⁡(M)⋅M2 …(i)det⁡(I)=(det⁡(M))5       since kA=k3A if A is 3×3 matrix1=det⁡(M)      ⋯(ii) From (i)  I=M2(adj⁡M)2=adj⁡M2=adj⁡I=I
Watch 3-min video & get full concept clarity
score_test_img

Get Expert Academic Guidance – Connect with a Counselor Today!

whats app icon