Let $A=\left(\begin{array}{ccc}1 & -1 & 1 \\ 2 & 1 & -3 \\ 1 & 1 & 1\end{array}\right)$ and $B=\left(\begin{array}{ccc}4 & 2 & 2 \\ -5 & 0 & \alpha \\ 1 & -2 & 3\end{array}\right)$. If $B$ is the inverse of matrix $A$, then $\alpha$ is

JEE Main · 2004 · 24 Apr 2004 · Offline · Matrices

Let

A = 121 - 1 11 1 - 3 1

and

B = 4 - 5 1 20 - 2 2 α 3

. If

B

is the inverse of matrix

A

, then

α

Answer: (B)

B

is the inverse of

A

then

A B = I

, so every off-diagonal entry of

A B

must vanish. Look at the entry in row

2

, column

3

: it is the dot product of row

2

A

, namely

(2, 1, - 3)

, with column

3

B

, namely

(2, α, 3)

. This gives

2 (2) + 1 (α) + (- 3) (3) = α - 5

, and setting it to zero gives

α = 5

JEE Main · 2004 · 24 Apr 2004 · Offline · Single correct option