Test by Bikram | Mathematics | Test 2 | Question: 6

Question

If $A$ is a $4$ rowed square matrix such that $\mid  A \mid = 4$, then $\text{adj (adj } A)$ is equal to _____.

• A. $2A$
• B. $4A$
• C. $8A$
• D. $16A$

Answer 1

Adj(Adj(A)) =|A|^(n-2).A

[ n = dimension size , in this case is 4]

 = |A|^(4-2).A = |A|^2 . A = 16A

Comments

@Harsh. How can i derive this formula using following identity:-

 

adj(A)⋅A=detA⋅In

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@Bikram sir,can you help in above doubt?

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@ rahul sharma 5 

read this https://math.stackexchange.com/questions/92837/proof-mathrmadj-mathrmadja-mathrmdetan-2-cdot-a-for-a

video , see this   https://www.youtube.com/watch?v=Vej0dRB1MGw