Question

Let $A = \begin{bmatrix} 1 & - 1 & 1 \\ 2 & 1 & - 3 \\ 1 & 1 & 1 \end{bmatrix}$and $10.B = \begin{bmatrix} 4 & 2 & 2 \

• 5 & 0 & \alpha \ 1 & - 2 & 3 \end{bmatrix}$. If B is the inverse of matrix A, then$\alpha$is

• A. 5
• B. –1
• C. 2
• D. –2

Answer 1

Answer: (A)

5

Answer 2

We have, $A = \begin{bmatrix} 1 & - 1 & 1 \

• 2 & 1 & - 3 \ 1 & 1 & 1 \end{bmatrix}$, ∴$|A| = 1(4) + 1(5) + 1(1) = 10$

and $adj(A) = \begin{bmatrix} 4 & 2 & 2 \

• 5 & 0 & 5 \ 1 & - 2 & 3 \end{bmatrix}$

Then $A^{- 1} = \frac{1}{10}\begin{bmatrix} 4 & 2 & 2 \

• 5 & 0 & 5 \ 1 & - 2 & 3 \end{bmatrix}$

According to question, B is the inverse of matrix A. Hence $\alpha = 5$