# JEE Main & Advanced Mathematics Matrices Scalar Multiplication of Matrices

Scalar Multiplication of Matrices

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.

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