TS EAMCET · Maths · Matrices
If a matrix is chosen at random from the set of all \(3 \times 3\) non zero matrices whose entries are the elements of the set \(\{-1,0,1\}\), then the probability that the matrix is skew symmetric is
- A \(\frac{1}{729}\)
- B \(\frac{1}{757}\)
- C \(\frac{1}{703}\)
- D \(\frac{1}{742}\)
Answer & Solution
Correct Answer
(B) \(\frac{1}{757}\)
Step-by-step Solution
Detailed explanation
Total numbers of non-zero matrices \(=3^9-1\) Now to make skew symmetric, diagonal elements must be 0 \(\left[\begin{array}{ccc}0 & a & b \\ -a & 0 & c \\ -b & -c & 0\end{array}\right]\) also if we take \(a\) from \(-1,0\) or 1 then \(-a\) is also fixed, similarly for \(b\)…
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