Can I assign an array itself to an element like this, or how can I achieve this.
No
You can do
int cells[4][4] =
{
{0, 1, 0, 1},
{1, 0, 1, 0},
{1, 1, 1, 1},
{0, 0, 0, 0}
};
void setup()
{
Serial.begin(115200);
cells[1][0] = 1;
cells[1][1] = 1;
cells[1][2] = 0;
cells[1][3] = 0;
}
Note that the array index for both dimensions starts at 0 not 1 as your attempted code might suggest.