Test Index

GUJCET 2026 Math Paper

© examsnet.com

Question : 21 of 40

Marks: +1, -0

If the inverse matrix of

A = \begin{bmatrix} 2 & 3 \\ 1 & -4 \end{bmatrix}

A^{-1} = \begin{bmatrix} a & 3/11 \\ 1/11 & b \end{bmatrix}

a+b=

. . . . . . .

$-\frac{2}{11}$
$\frac{2}{11}$
$\frac{6}{11}$
$-\frac{6}{11}$

Solution:

Concept:

The inverse of a

2\times2

matrix is calculated using its determinant and adjugate.

Explanation:

For

A=\begin{bmatrix}2&3\\1&-4\end{bmatrix}

,

|A|=(2)(-4)-(3)(1)=-11

So,

A^{-1}=\frac{1}{|A|}\begin{bmatrix}-4&-3\\-1&2\end{bmatrix}

A^{-1}=\begin{bmatrix}4/11&3/11\\1/11&-2/11\end{bmatrix}

Comparing with the given

A^{-1}

,

a=4/11

and

b=-2/11

.

Therefore,

a+b=\frac{4}{11}-\frac{2}{11}=\frac{2}{11}

Answer:

\frac{2}{11}

, so the correct option is B.

© examsnet.com

Go to Question:

Prev Question

Next Question