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\( 0_{m \times n} \)  denotes the  \( m \times n \)  zero matrix , with all entries zero. \( I_{n} \)  denotes the \( n \times n \)  identity matrix , with \( I_{ij}= \cases{ 1 & i = j \cr 0 & i $\ne$ j } \) For example;  \( 0_{2 \times 3} = \left\lbrack \matrix{ 0 & 0 & 0 \cr 0 & 0 & 0 } \right\rbrack, \)  \(  I_{2} =  \left\lbrack \matrix{ 1 & 0 \cr 0 & 1 } \right\rbrack \) Transpose of Matrix  \( A = \left\lbrack \matrix{ a & b & c \cr d & e & f } \right\rbrack {⇒}  \)  \({A^T} = \left\lbrack \matrix{ a & d \cr b & e \cr c & f } \right\rbrack \) Summation of Matrices (entrywise) \( \left\lbrack \matrix{ a & b \cr c & d } \right\rbrack + \left\lbrack \matrix{ x & y \cr z & t} \right\rbrack = \left\lbrack \matrix{ a+x & b+y \cr c+z & d+t } \right\rbrack\) Subtraction of Matrices (entrywise) \( \left\lbrack \matrix{ a & b \cr c & d } \right\rbrack - \left\lbrack \matrix{ x