Question

If A is a square matrix of order 5 and $9A^{-1}=4A^T$ then |adj (adj (adj A))I (where $A^{-T}$ and adj(A) denotes the inverse, transpose and adjoint of matrix A respectively) contains: $(log3=0.477,log2=0.303)$

• A. 56 digits
• B. 60 digits
• C. 58 digits
• D. 53 digits

Answer 1

The correct option is A 56 digits

$9A^{-1}=4A^T\Rightarrow |9A^{-1}|=|4A^T|\Rightarrow 9^5\times \frac{1}{|A|}=4^5|A|\Rightarrow |A|={\left(\frac{3}{2}\right)}^5$

|adj adj adj A| $=|A{|}^{4^3}={\left(\frac{3}{2}\right)}^{320}$

No. of digits in |adj adj adj A| $=\left[log{\left(\frac{3}{2}\right)}^{320}\right]+1=56$. ([.] denotes greatest integer function).