The number of all non-zero matrices of order 2 × 3 with each entry -1, 0, 1 is:

728

$\text{Order of matrix}=2\times3.$

$\text{Total entries}=6.$

$\text{Each entry can be }-1,0,1.$

$\text{Number of possible matrices}=3^6.$

$=729.$

$\text{Zero matrix}=1.$

$\text{Non-zero matrices}=729-1.$

$=728.$

$\text{Number of non-zero matrices}=728.$