If A= [ rr 2 & 3 5 & -2 ] be such that A^ -1 =k A, then k equals - Vidyadip

MCQ

If $A=\left[\begin{array}{rr}2 & 3 \\ 5 & -2\end{array}\right]$ be such that $A^{-1}=k A$, then $k$ equals

A
19
✓
$\frac{1}{19}$
C
$-\frac{1}{19}$
D
-19

✓

Answer

Correct option: B.

$\frac{1}{19}$

(b) $\frac{1}{19}$
Explanation:
A $=\left[\begin{array}{ll}2 & 3 \\ 5 & -2\end{array}\right]$
Using adjoint matrix
$
\begin{array}{l}
A^{-1}=\frac{-1}{19}\left[\begin{array}{ll}
-2 & -3 \\
-5 & 2
\end{array}\right] \\
A^{-1}=\frac{1}{19}\left[\begin{array}{cc}
2 & 3 \\
5 & -2
\end{array}\right]=\frac{1}{19} A \\
k=\frac{1}{19}
\end{array}
$

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