Properties of Transpose and Conjugate Transpose of a Matrix
Matrices and Determinants of Class 12
Properties of Transpose and Conjugate Transpose of a Matrix
(i) (A′)′ = A, (A*)* = A
(ii) (A + B)′ = A′ + B′, (A + B)* = A* + B*
(iii) (kA)′ = kA′, (kA)* = 
A*, k being a scalar.
(iv) (AB)′ = B′A′, (AB)* = B* A*
- Definition of a Matrix
- Special Types of Matrices
- Equality of Two Matrices
- Addition of Matrices
- Multiplication of Matrices
- Properties of Matrix Multiplication
- Transpose of a Matrix
- Transposed Conjugate of a Matrix
- Properties of Transpose and Conjugate Transpose of a Matrix
- Some More Special Type of Matrices
- Adjoint Of A Square Matrix
- Inverse of a Square Matrix
- Definition of a Determinant
- Value of a Determinant
- Properties of Determinants
- System of Linear Simultaneous Equations
- System of Linear Non Homogenous Simultaneous Equations
- Exercise 1
- Exercise 2
- Exercise 3
- Exercise 4
- Exercise 5
- Exercise 6
- Exercise 7
- Exercise 8
