In the matrix $A = \left[ {\begin{array}{cccccccccccccccccccc}a&1&x\\2&{\sqrt 3 }&{{x^2} - y}\\0&5&{\frac{{ - 2}}{5}}\end{array}} \right]$, write

(i) the order of the matrix A.

(ii) the number of elements.

(iii) elements ${a_{23}},{a_{31}}$ and ${a_{12}}$

We have $A = \left[ {\begin{array}{cccccccccccccccccccc}a&1&x\\2&{\sqrt 3 }&{{x^2} - y}\\0&5&{\frac{{ - 2}}{5}}\end{array}} \right]$

(i) the order of matrix $A = 3 \times 3$

(ii) the number of elements $= 3 \times 3 = 9$

[since, the number of elements in an ${\rm{m}} \times {\rm{n}}$

matrix will be equal to ${\rm{m}} \times {\rm{n}} = {\rm{mn}}$]

(iii) ${a_{23}} = {x^2} - y,$ ${a_{31}} = 0,$ ${a_{12}} = 1$

[since, As we know, ${a_{ij}}$,

is a representation of element lying in the $i$ h row and $j$th column]