2.1 (a) Addition and subtraction of Matrices:

1.1 Type of Matrices
1.2 Trace of a Matrix:
1.3 Transpose of a Matrix
1.4 Conjugate of a Matrix

2.1 (a) Addition and subtraction of Matrices:
2.2 (b) Multiplication of Matrices:

3.1 (a) Symmetric Matrix:
3.2 (b) Skew Symmetric Matrix:
3.3 (c) Hermitian matrix:
3.4 (d) Skew Hermitian Matrix:
3.5 (e) Singular and Non-singular Matrices:
3.6 (f) Orthogonal Matrix :
3.7 (g) Idempotent Matrix :
3.8 (h) Unitary Matrix :
3.9 (i) Involuntary Matrix:
3.10 (j) Nilpotent Matrix:

4.1 Minors & Cofactors
4.2 Properties of Determinant

5.1 Elementary row Transformations

6.1 Properties of Inverse of a Matrix
6.2 Elementary row Transformations

8.1 Echelon form of a Matrix
8.2 Rank of a Matrix

Any two matrices can be added or subtracted if they are of the same order and the resulting matrix is of the same order.

If $A = \left[ {\begin{array}{c} \alpha &\beta &\gamma \\ \theta &\phi &\psi \end{array}} \right]\& B = \left[ {\begin{array}{c} a&b&c \\ x&y&z \end{array}} \right]$,

Then $A + B = \left[ {\begin{array}{c} {\alpha + a}&{\beta + b}&{\gamma + c} \\ {\theta + x}&{\phi + y}&{\psi + z} \end{array}} \right]$

and $A - B = \left[ {\begin{array}{c} {\alpha - a}&{\beta - b}&{\gamma - c} \\ {\theta - x}&{\phi - y}&{\psi - z} \end{array}} \right]$

If $A = \left[ {\begin{array}{c} 2&3&4 \\ { - 3}&4&8 \end{array}} \right]\& B = \left[ {\begin{array}{c} { - 1}&4&7 \\ { - 3}&{ - 2}&5 \end{array}} \right]$

then find $A + B$

$A + B = \left[ {\begin{array}{c} 2&3&4 \\ { - 3}&4&8 \end{array}} \right] + \left[ {\begin{array}{c} { - 1}&4&7 \\ { - 3}&{ - 2}&5 \end{array}} \right]$

$ = \left[ {\begin{array}{c} {2 - 1}&{3 + 4}&{4 + 7} \\ { - 3 - 3}&{4 - 2}&{8 + 5} \end{array}} \right]$

$ = \left[ {\begin{array}{c} 1&7&{11} \\ { - 6}&2&{13} \end{array}} \right]$

If $A = \left[ {\begin{array}{c} 2&3&4 \\ { - 3}&4&8 \end{array}} \right]\& \, B = \left[ {\begin{array}{c} { - 1}&4&7 \\ { - 3}&{ - 2}&5 \end{array}} \right]$

then find $A - B$

$$A - B = \left[ {\begin{array}{c} 2&3&4 \\ { - 3}&4&8 \end{array}} \right] - \left[ {\begin{array}{c} { - 1}&4&7 \\ { - 3}&{ - 2}&5 \end{array}} \right]$$

$$ = \left[ {\begin{array}{c} {2 + 1}&{3 - 4}&{4 - 7} \\ { - 3 + 3}&{4 + 2}&{8 - 5} \end{array}} \right]$$

$$ = \left[ {\begin{array}{c} 3&{ - 1}&{ - 3} \\ 0&6&3 \end{array}} \right]$$