# Compute A B and B A, which ever exists when

Question:

Compute $A B$ and $B A$, which ever exists when

Solution:

Matrix A is of order $1 \times 4$ and Matrix $B$ is of order $4 \times 1$

To find : matrices $A B$ and $B A$

Formula used :

Where $c_{i j}=a_{i 1} b_{1 j}+a_{i 2} b_{2 j}+a_{i 3} b_{3 j}+\ldots \ldots \ldots \ldots \ldots . .+a_{i n} b_{n j}$

If $A$ is a matrix of order $a \times b$ and $B$ is a matrix of order $c \times d$, then matrix $A B$ exists and is of order $a \times d$, if and only if $b=$ $c$

If $A$ is a matrix of order $a \times b$ and $B$ is a matrix of order $c \times d$, then matrix $B A$ exists and is of order $c \times b$, if and only if $d=$ a

For matrix $A B, a=1, b=4, c=4, d=1$, matrix $A B$ exists and is of order $1 \times 1$, as

$b=c=4$

Matrix $\mathrm{AB}=[1+4+9+16]=[30]$

Matrix $A B=[30]$

Matrix $\mathrm{AB}=[30]$

For matrix $\mathrm{BA}, \mathrm{a}=1, \mathrm{~b}=4, \mathrm{c}=4, \mathrm{~d}=1$, matrix $\mathrm{BA}$ exists and is of order $4 \times 4$,as

$d=a=1$

Matrix BA $=\left[\begin{array}{cccc}1 & 2 & 3 & 4 \\ 2 & 4 & 6 & 8 \\ 3 & 6 & 9 & 12 \\ 4 & 8 & 12 & 16\end{array}\right]$