First slide

Applications of determinant

Question

$If A = [\begin{array}{rr} - 6 5 \\ - 7 6 \end{array}] and A B = I then B =$

Moderate

A

$[\begin{matrix} 6 & 5 \\ 7 & 6 \end{matrix}]$
B

$[\begin{matrix} - 6 & 5 \\ - 7 & 6 \end{matrix}]$
C

$[\begin{matrix} - 6 & - 5 \\ - 7 & 6 \end{matrix}]$
D

$[\begin{matrix} 6 & 5 \\ - 7 & - 6 \end{matrix}]$

Solution

$A B = I$
$\begin{array}{l} \Rightarrow B = A^{- 1} \\ = \frac{1}{- 36 + 35} [\begin{array}{cc} 6 & - 5 \\ 7 & - 6 \end{array}] \\ = [\begin{array}{cc} - 6 & 5 \\ - 7 & 6 \end{array}] \end{array}$

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