Matrices And Determinants Ques 44
Which of the following is(are) NOT the square of a $3 \times 3$ matrix with real entries?
(a) $ \begin{bmatrix}1 & 0 & 0\ 0 & 1 & 0\ 0 & 0 & 1\end{bmatrix}$ 0 & 1 & 0 \\ 0 & 0 & -1\end{bmatrix}$
(b) $ \begin{bmatrix}1 & 0 & 0\ 0 & 1 & 0\ 0 & 0 & 1\end{bmatrix}$ 0 & -1 & 0 \\ 0 & 0 & -1\end{bmatrix}$
(c) $ \begin{bmatrix}-1 & 0 & 0\ 0 & -1 & 0\ 0 & 0 & -1\end{bmatrix}$ 0 & -1 & 0 \\ 0 & 0 & -1\end{bmatrix}$
(d) $ \begin{bmatrix}1 & 0 & 0\ 0 & 1 & 0\ 0 & 0 & 1\end{bmatrix}$ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$
(2017 Adv.)
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Answer:
Correct Answer: 44.(a,c)
Solution:
Formula:
Properties of matrix multiplication:
For a matrix to be square of another matrix its determinant should be non-zero.
(a) and (c) $\rightarrow$ Correct
(b) and (d) $\rightarrow$ Incorrect
BETA
