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The number of possible matrices of order 3 × 3 with each entry 2 or 0 is :

A. 9 

B. 27 

C. 81 

D. none of these.

1 Answer

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Best answer

(D). none of these.

Let A = \(\begin{bmatrix} a_{11} & a_{12} & a_{13} \\[0.3em] a_{21} & a_{22} & a_{23} \\[0.3em] a_{31} &a_{32} & a_{33} \end{bmatrix}\)

Elements = 9 Order = 3 × 3 

Every item in this matrix can be filled in two ways either by 0 or by 2. 

Possible Matrices = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 512 

Option (D) is the answer.

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