The number of diagonal matrices of order 3 with elements either 1 or 2, is:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 8
In a diagonal matrix all the non-diagonal elements are 0, so “elements either 1 or 2” refers to the three diagonal elements \( a_{11} \), \( a_{22} \), \( a_{33} \).
Each of them can be chosen in 2 ways, independently of the others:
\( \displaystyle \text{Number of matrices}=2\times 2\times 2 \)
\( \displaystyle =8 \)