Adj

Engineering

Mathematics

Inverse of a Matrix

Properties of Determinant

Transpose and Adjoint of a Matrix

Question

Adj $(Adj [\begin{array}{cc} 2 & - 3 \\ 4 & 6 \end{array}]) =$

$[\begin{array}{cc} - 6 & - 3 \\ 4 & - 2 \end{array}]$

$[\begin{array}{cc} 6 & 3 \\ - 4 & 2 \end{array}]$

$[\begin{array}{cc} - 6 & 3 \\ - 4 & - 2 \end{array}]$

$[\begin{array}{cc} 2 & - 3 \\ 4 & 6 \end{array}]$

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Adjoint of matrix is given by

[\begin{array}{cc} M_{11} & - M_{12} \\ - M_{21} & M_{22} \end{array}]

Here M₁₁ = 6

M₁₂ = 4

M₂₁ = – 3

M₂₂ = 2

So adjoint of the matrix is

[\begin{array}{cc} 6 & - 4 \\ 3 & 2 \end{array}]

Again adjoint of this matrix is

[\begin{array}{cc} 2 & - 3 \\ 4 & 6 \end{array}]

Hence the answer is option A.