Question

If \(3\times3\) matrices are formed by using \(0,\pm1,\pm2\) as their elements, then the number of matrices whose trace is \(0\) is

• A. \(19\cdot5^6\)
• B. \(16\cdot5^9\)
• C. \(15\cdot5^6\)
• D. \(14\cdot5^8\)

Hint:

For matrix counting problems, \[ \boxed{\text{Total count}= (\text{Valid diagonal choices}) \times (\text{Choices for remaining entries})} \] The off-diagonal entries are independent of the trace.

Answer 1

The Correct Option is A