Question
Question: If A = \(\frac{1}{9}\) \(\begin{bmatrix} - 8 & 1 & 4 \\ 4 & 4 & 7 \\ 1 & - 8 & 4 \end{bmatrix}\) th...
If A = 91 $\begin{bmatrix}
- 8 & 1 & 4 \ 4 & 4 & 7 \ 1 & - 8 & 4 \end{bmatrix}$ then A is –
A
Involutary matrix
B
Idempotent matrix
C
Orthogonal matrix
D
Nilpotent matrix
Answer
Orthogonal matrix
Explanation
Solution
- 8 & 4 & 1 \\
1 & 4 & - 8 \\
4 & 7 & 4
\end{bmatrix}$$
$$AA^{T} = \frac{1}{81}\begin{bmatrix}
81 & 0 & 0 \\
0 & 81 & 0 \\
0 & 0 & 81
\end{bmatrix} = I$$
Ž A is orthogonal matrix
Hence (3) is correct.