Let be the set containing all matrices with entries from . The total number of matrices such that the sum of all the diagonal elements of is 6 is ____________. ...

Sum of all diagonal elements is equal to sum of square of each element of the matrix. i.e., A = [ a_1 & a_2 & a_3 b_1 & b_2 & b_3 c_1 & c_2 & c_3 ] then t_r\,(A\,.\,A^T) = a_1^2 + a_2^2 + a_3^2 + b_1^2 + b_2^2 + b_3^2 + c_1^2 + c_2^2 + c_3^2 a_i,b_i,c_i \ - 1,0,1\ fo...

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Let S be the set containing all 3 x 3 matrices with entries : null (Mathematics) | DivineJEE

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Let $S$ be the set containing all $3 \times 3$ matrices with entries from $\{-1,0,1\}$ . The total number of matrices $A \in S$ such that the sum of all the diagonal elements of $A^{\mathrm{T}} A$ is 6 is ____________.

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