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  • please solve rd sharma class 12 chapter adjoint and inverse of a matrix exercise multiple choice questions question 4 maths textbook solution

please solve rd sharma class 12 chapter adjoint and inverse of a matrix exercise multiple choice questions  question 4 maths textbook solution

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\text { (b) }\left[\begin{array}{cc} d & -b \\ -c & a \end{array}\right]

Given: s=\left[\begin{array}{cc} a & b \\ c & d \end{array}\right]

Hint:  find adjoint S by finding cofactors and transposing it.

Solution :

 \begin{aligned} &S=\left[\begin{array}{ll} a & b \\ c & d \end{array}\right] \\ &C_{11}=(-1)^{1+1} d=d \\ &C_{12}=(-1)^{1+2} c=-c \\ &C_{21}=(-1)^{2+1} b=-b \\ &C_{22}=(-1)^{2+2} a=a \\ &\text { Adj } S=\left[\begin{array}{cc} d & -c \\ -b & a \end{array}\right]^{T}=\left[\begin{array}{cc} d & -b \\ -c & a \end{array}\right] \end{aligned}

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