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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.

**Complete step-by-step answer:**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.

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