**Category : **JEE Main & Advanced

Let \[A={{[{{a}_{ij}}]}_{m\times n}}\]be a matrix and k be a number, then the matrix which is obtained by multiplying every element of A by k is called scalar multiplication of A by k and it is denoted by kA.

Thus, if \[A={{[{{a}_{ij}}]}_{m\times n}}\], then \[kA=Ak={{[k{{a}_{ij}}]}_{m\times n}}\].

**Properties of scalar multiplication**

If A, B are matrices of the same order and \[\lambda ,\,\mu \] are any two scalars then

(i) \[\lambda (A+B)=\lambda A+\lambda B\]

(ii) \[(\lambda +\mu )A=\lambda A+\mu A\]

(iii) \[\lambda (\mu A)=(\lambda \mu A)=\mu (\lambda A)\]

(iv) \[(-\lambda A)=-(\lambda A)=\lambda \,(-A)\]

- All the laws of ordinary algebra hold for the addition or subtraction of matrices and their multiplication by scalars.

*play_arrow*Definition*play_arrow*Order of a Matrix*play_arrow*Equality of Matrices*play_arrow*Types of Matrices*play_arrow*Trace of a Matrix*play_arrow*Addition and Subtraction of Matrices*play_arrow*Scalar Multiplication of Matrices*play_arrow*Multiplication of Matrices*play_arrow*Positive Integral Powers of a Matrix*play_arrow*Transpose of a Matrix*play_arrow*Special Types of Matrices*play_arrow*Adjoint of a Square Matrix*play_arrow*Inverse of a Matrix*play_arrow*Rank of Matrix*play_arrow*Echelon Form of a Matrix*play_arrow*Homogeneous and Non-homogeneous Systems of Linear Equations*play_arrow*Consistency of a System of Linear Equation \[\mathbf{AX=B,}\] where \[\mathbf{A}\] is a square matrix*play_arrow*Cayley-Hamilton Theorem*play_arrow*Geometrical Transformations*play_arrow*Matrices of Rotation of Axes

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