Question

# The order of the matrix $A$ is $3 \times 5$ and that of $B$ is $2 \times 3$. The order of the matrix $BA$ is:A. $2 \times 3$B.$\;\;3 \times 2$C. $2 \times 5$D. $5 \times 2$

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Hint: We have given two matrices $A$ and $B$. The order of the matrix $A$ is $3 \times 5$ and the order of the matrix is $2 \times 3$. We have to find the order of the matrix $BA$. We know that two matrices can be multiplied to each other if the number of columns of pre prematrix is equal to the number of columns in the post matrix.

Firstly we find the result by taking two general matrix then we will do it for matrix $A$ and $B$
Let ${\left[ P \right]_{m \times n}}$ and ${\left[ Q \right]_{n \times q}}$ be two matrix where is order of matrix $P$ and $n \times q$ is the order of matrix $Q$.
Now the number of columns in the matrix $P$ is equal to the number of rows in the matrix $Q$. So multiplication is possible.
Let $PQ$ be the resulting matrix.
Order of $PQ$ will be the product of the number of rows of $P$ and number of columns of $Q$.
So order of $PQ$ is $m \times q$
Now order of $A$ is $3 \times 5$
And order of $B$ is $2 \times 3$
In matrix A, According to the given order 3 rows and 5 columns is present
In matrix B, According to the given order 2 rows and 3 columns is present
So order of $BA$ will be $2 \times 5$
So option $(c)$ is correct.

Note: Matrix is a rectangular arrangement of numbers, expression or letters which are arranged in row and column. If the matrix has $n$ row and $m$ column there it is called $n \times m$ matrix where $m \times n$ is the order of the matrix. Matrices are used to solve different equations in two variables. Matrices which have an equal number of rows and columns known as square matrices.