If k is a scalar and I is a unit matrix of or | vedclass

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(B) Let $I$ be the identity matrix of order $3 	imes 3$,given by $I = \begin{bmatrix} 1 & 0 & 0 \ 0 & 1 & 0 \ 0 & 0 & 1 \end{bmatrix}$.Then,$kI = \

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$k^2I$

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(B) Let $I$ be the identity matrix of order $3 	imes 3$,given by $I = \begin{bmatrix} 1 & 0 & 0 \ 0 & 1 & 0 \ 0 & 0 & 1 \end{bmatrix}$.Then,$kI = \begin{bmatrix} k & 0 & 0 \ 0 & k & 0 \ 0 & 0 & k \end{bmatrix}$.The adjoint of a diagonal matrix $D = 	ext{diag}(a, b, c)$ is given by $	ext{diag}(bc, ac, ab)$.Here,$adj(kI) = \begin{bmatrix} k 	imes k & 0 & 0 \ 0 & k 	imes k & 0 \ 0 & 0 & k 	imes k \end{bmatrix} = \begin{bmatrix} k^2 & 0 & 0 \ 0 & k^2 & 0 \ 0 & 0 & k^2 \end{bmatrix} = k^2 I$.Alternatively,using the property $adj(kA) = k^{n-1} adj(A)$ where $n$ is the order of the matrix,for $A=I$ and $n=3$,we get $adj(kI) = k^{3-1} adj(I) = k^2 I$.

If $k$ is a scalar and $I$ is a unit matrix of order $3$,then $adj(kI) = $

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