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Maths-

General

Easy

Question

If A = $open square brackets table row 1 2 row 3 5 end table close square brackets$ , then A^–1 is equal to :

$[\begin{matrix} 5 & 2 \\ 3 & 1 \end{matrix}]$
$[\begin{matrix} - 5 & 3 \\ 2 & - 1 \end{matrix}]$
$[\begin{matrix} - 5 & 2 \\ 3 & - 1 \end{matrix}]$
none of these

The correct answer is: $open square brackets table row cell – 5 end cell 2 row 3 cell – 1 end cell end table close square brackets$

A^–1 = $fraction numerator a d j A over denominator vertical line A vertical line end fraction$
$because$ |A| = – 1
adj A = $open square brackets table row 5 cell – 2 end cell row cell – 3 end cell 1 end table close square brackets$
so, A^–1 = $open square brackets table row cell – 5 end cell 2 row 3 cell – 1 end cell end table close square brackets$

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