For matrix A = [ lll 2 & 0 & 0 0 & 3 & 0 0 & 0 & 4 ], ( A ^ -1 )^… - Vidyadip

MCQ

For matrix $A =\left[\begin{array}{lll}2 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 4\end{array}\right],\left( A ^{-1}\right)^2=$ __________ .

A
$\left[\begin{array}{ccc}-\frac{1}{4} & 0 & 0 \\ 0 & -\frac{1}{9} & 0 \\ 0 & 0 & -\frac{1}{16}\end{array}\right]$
B
$\left[\begin{array}{ccc}-4 & 0 & 0 \\ 0 & -9 & 0 \\ 0 & 0 & -16\end{array}\right]$
✓
$\left[\begin{array}{ccc}\frac{1}{4} & 0 & 0 \\ 0 & \frac{1}{9} & 0 \\ 0 & 0 & \frac{1}{16}\end{array}\right]$
D
$\left[\begin{array}{ccc}4 & 0 & 0 \\ 0 & 9 & 0 \\ 0 & 0 & 16\end{array}\right]$

✓

Answer

Correct option: C.

$\left[\begin{array}{ccc}\frac{1}{4} & 0 & 0 \\ 0 & \frac{1}{9} & 0 \\ 0 & 0 & \frac{1}{16}\end{array}\right]$

C

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