Question

A= [2, 3; 2, 1], B=[3; 5]. Find AB & BA if possible

Answer 1

The value of AB is
`\left[\begin{array}{ccc}21\\11\end{array}\right]` and it's not possible to multiply BA.

Explanation:

Consider the provided matrices.

`A=\left[\begin{array}{ccc}2&3\\2&1\end{array}\right]`,
`B=\left[\begin{array}{ccc}3\\5\end{array}\right]`

Two matrices can be multiplied if and only if first matrix has an order m × n and second matrix has an order n × v.

Multiply AB

Matrix A has order 2 × 2 and matrix B has order 2 × 1. So according to rule we can multiply both the matrix as shown:

`AB=\left[\begin{array}{ccc}2&3\\2&1\end{array}\right] \left[\begin{array}{ccc}3\\5\end{array}\right]`

`AB=\left[\begin{array}{ccc}2* 3+3* 5\\2* 3+1* 5\end{array}\right]`

`AB=\left[\begin{array}{ccc}6+15\\6+5\end{array}\right]`

`AB=\left[\begin{array}{ccc}21\\11\end{array}\right]`

Hence, the value of AB is
`\left[\begin{array}{ccc}21\\11\end{array}\right]`

Now calculate the value of BA as shown:

Multiply BA

Matrix B has order 2 × 1 and matrix A has order 2 × 2. So according to rule we cannot multiply both the matrix.

We can multiply two matrix if first matrix has an order m × n and second matrix has an order n × v.

That means number of column of first matrix should be equal to the number of rows of second matrix.

Hence, it's not possible to multiply BA.