If a 3 3 matrix B has its inverse equal to B, then B^2= - Vidyadip

MCQ

If a $3 \times 3$ matrix $B$ has its inverse equal to $B$, then $B^2=$

A
$\left[\begin{array}{lll}0 & 1 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 1\end{array}\right]$
B
$\left[\begin{array}{lll}1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 0 & 1\end{array}\right]$
C
$\left[\begin{array}{lll}1 & 0 & 1 \\ 0 & 1 & 0 \\ 0 & 0 & 0\end{array}\right]$
✓
$\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{array}\right]$

✓

Answer

Correct option: D.

$\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{array}\right]$

(d) $\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{array}\right]$
Hint:
$
\begin{aligned}
& B ^{-1}= B \\
& \therefore B ^2= B \cdot B ^{-1}=1
\end{aligned}
$

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