If A= [(( cos x),(sin x)),((−sin x),(cos x)) ] and A adj A = k [(1,0),(0,1) ], then the value of k is


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Question Number 42728 by RANGAM kumar last updated on 01/Sep/18

$If A = [\begin{matrix} \cos x & \sin x \\ - \sin x & \cos x \end{matrix}] and$ $A adj A = k [\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}], then the value of k is$
	Answered by math1967 last updated on 01/Sep/18

	$a d j A = {[\begin{matrix} c o s x & s i n x \\ - s i n x & c o s x \end{matrix}]}^{t} = [\begin{matrix} c o s x & - s i n x \\ s i n x & c o s x \end{matrix}]$ $∴ [\begin{matrix} c o s x & s i n x \\ - s i n x & c o s x \end{matrix}] [\begin{matrix} c o s x & - s i n x \\ s i n x & c o s x \end{matrix}]$ $[\begin{matrix} {c o s}^{2} x + {s i n}^{2} x & 0 \\ 0 & {s i n}^{2} x + {c o s}^{2} x \end{matrix}]$ $[\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}] = 1 . [\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}] ∴ k = 1$
	Answered by RANGAM kumar last updated on 02/Sep/18

	$zza$
	Commented by math1967 last updated on 02/Sep/18

	$? ? ? ? ? ? w h a t i s w r o n g ?$
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