The sum of elements of the matrix

[jeremjen]

Matrix A has size [math]3×2[/math], and matrix B has size .[math]2×3[/math]. It is known that AB = [math]\begin{matrix} 8 & 2& -2\\ 2 & 5& 4\\ -2 & 4& 5 \end{matrix}[/math] and the matrix BA is nondegenerate. If C=BA, then the sum of all elements of the matrix C equals _________

 

[Deleted member 4993]

Matrix A has size [math]3×2[/math], and matrix B has size .[math]2×3[/math]. It is known that AB = [math]\begin{matrix} 8 & 2& -2\\ 2 & 5& 4\\ -2 & 4& 5 \end{matrix}[/math] and the matrix BA is nondegenerate. If C=BA, then the sum of all elements of the matrix C equals _________

How many elements does matrix BA have? What is the property of a non-degenerate matrix?

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