Matrix Equality

Two Matrices ${\hbox{\sf A}}$ and ${\hbox{\sf B}}$ are said to be equal Iff

$$a_{ij} \equiv b_{ij}$$

for all $i, j$. Therefore,

$$\left[{\matrix{1 & 2\cr 3 & 4\cr}}\right]=\left[{\matrix{1 & 2\cr 3 & 4\cr}}\right],$$

while

$$\left[{\matrix{1 & 2\cr 3 & 4\cr}}\right]\not=\left[{\matrix{0 & 2\cr 3 & 4\cr}}\right].$$