Consider A=⎡⎢⎣a210b00−3c⎤⎥⎦ where a,b,c are the roots of the equation x3−3x2+2x−1=0. If matrix B is such that AB=BA,|A+B−2I|≠0 and A2−B2=4I−4B, where I is the 3×3 identity matrix, then the value of √det(B) is

Consider A=⎡⎢⎣a210b00−3c⎤⎥⎦ where a,b,c are the roots of

1.	Consider A=⎡⎢⎣a210b00−3c⎤⎥⎦ where a,b,c are the roots of the equation x3−3x2+2x−1=0. If matrix B is such that AB=BA,\|A+B−2I\|≠0 and A2−B2=4I−4B, where I is the 3×3 identity matrix, then the value of √det(B) is
Answer» Consider $A = ⎡ ⎢ ⎣ \begin{matrix} a & 2 & 1 0 & b & 0 0 & - 3 & c \end{matrix} ⎤ ⎥ ⎦$ where $a, b, c$ are the roots of the equation $x^{3} - 3 x^{2} + 2 x - 1 = 0.$ If matrix $B$ is such that $A B = B A, \| A + B - 2 I \| \neq 0$ and $A^{2} - B^{2} = 4 I - 4 B,$ where $I$ is the $3 \times 3$ identity matrix, then the value of $\sqrt{d e t (B)}$ is