Question

Let a be the square matrix of order 2 such that $A^2-4A+4I=0$ where I is an identify matrix of order 2. .If$B=A^5-4A^4+6A^3+4A^2+A$ then Det (B) is equal to

• A. 162
• B. $(162{)}^2$
• C. 256
• D. $(256{)}^2$

Answer 1

Answer: (B)

$(162{)}^2$

$A^2-4A+4I=O\Rightarrow (A-2I{)}^2=O\Rightarrow A=2I$
$B=A(A^4+4A^3+6A^2+4A+I)=A(A+I{)}^4=2I(3I{)}^4=162I$
det$\left(B\right)=(162{)}^2$