If A={pmatrix}5 & -2\\-1 & 3{pmatrix}, then Adjoint of Matrix A

Correct Answer is : (3215){pmatrix}3 & 2\\1 & 5{pmatrix}(3125)

{pmatrix}3 & -2\\-1 & 5{pmatrix}

{pmatrix}5 & 2\\-1 & 3{pmatrix}

{pmatrix}3 & -2\\1 & 5{pmatrix}

Correct Answer is : (3215){pmatrix}3 & 2\\1 & 5{pmatrix}(3125)

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Question : 31 of 36

Marks: +1, -0

A=\begin{pmatrix}5 & -2\\-1 & 3\end{pmatrix},

then Adjoint of Matrix A

Solution:

Concept:

The adjoint of a matrix is the transpose of its cofactor matrix.

Explanation:

For a

2 \times 2

matrix

A = \begin{pmatrix} a & b \\ c & d \end{pmatrix}

, the adjoint is

\begin{pmatrix} d & -b \\ -c & a \end{pmatrix}

Here,

a = 5

b = -2

c = -1

d = 3

Substitute:

\begin{pmatrix} 3 & -(-2) \\ -(-1) & 5 \end{pmatrix} = \begin{pmatrix} 3 & 2 \\ 1 & 5 \end{pmatrix}

Answer:

\begin{pmatrix} 3 & 2 \\ 1 & 5 \end{pmatrix}

, which matches option D.

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