Question

If AB=C WHERE B AND C ARE MATRICES OF ORDER 3×5 THEN THE ORDER OF MATRIX A IS A)3×5 B)3×3 C)5×5 D)5×3​

Answer 1

Answer:

LET order of A is x*y

Then order of AB can be obtain by

(x*y) (3*5) equivalent to (3*5)

Y=3 and x=3

Order of A is(3*3)

Answer 2

Concept:

We need to first recall the concept of multiplication of two matrices .

Let A = $[a_{ij}]_{m\times n}$ and B = $[b_{ij}]_{n\times p}$

Two such matrices are said to be conformable for multiplication if the number of columns in A is equal to the number of rows in B.

Then C = $[c_{ij}]_{m\times p}$ is said to be the product of the matrices A and B.

i.e. AB = C

A is said to be prefactor and B is said to be postfactor in the product AB.

Given:

A , B and C be three matrices such that AB = C and order of matrix B and C is 3 × 5.

To find:

The order of the Matrix A.

Solution:

Since, AB = C

     The number of rows of matrix A =  number of rows of matrix C

                                                           = 3

The number of columns of matrix A = number of rows of matrix B

                                                           = 3

Hence, Order of matrix A is 3 × 3.

Option (B) is correct choice.