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Question

If A=[5ab32]  and A adj A=AAT, then 5a + b is equal to

 


Your Answer
A
-1
Correct Answer
B
5
Your Answer
C
4
Your Answer
D
13

Solution

The correct option is B 5
Given, A=[5ab32] and A adj A=AAT
Clearly, A (adj A) = |A| I2
[ if A is square matrix of order n, then A(adj A) = (adj A) . A = |A| In]
=[5ab32]I2=(10a+3b)I2=(10a+3b)[1001]
[10a+3b0010+3b]           . . . (i)
and AAT=[5ab32][5a3b2]
AAT=[25a2+b215a2b15a2b13]     . . . (ii)
   A(adjA)=AAT
 [10a+3b0010a+3b]=[25a2+b215a2b15a2b13]         using Eqs. (i) and (ii)]
     15a - 2b = 0
   a=2b15                       . . . (iii)
and   10a + 3b = 13                     . . . (iv)
On substituting the value of 'a' from Eq. (iii) in Eq. (iv),. we get
10.(2b15)+3b=13   20b+45b15=13   65b15=13   b=3
Now, substituting the value of b in Eq. (iii), we get 5a = 2
Hence, 5a + b = 2 + 3 = 5

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