question_answer

Let\[A=\left[ \begin{matrix}    1 & -1 & 1  \\    2 & 1 & -3  \\    1 & 1 & 1  \\ \end{matrix} \right]\]and\[10B=\left[ \begin{matrix}    4 & 2 & 2  \\    -5 & 0 & \alpha   \\    1 & -2 & 3  \\ \end{matrix} \right].\]If B is the inverse of matrix A, then a is

A) -2                   

B) 1                             

C) 2                             

D) 5

Correct Answer: D

Solution :

Since, B is inverse of A i.e., \[B={{A}^{-1}}\]. So,                                                                                              \[(\because \,\,{{A}^{-1}}\,A=l)\]           and