If $A = [\begin{matrix} 2 & - 1 & 3 \\ - 4 & 5 & 1 \end{matrix}] and B = [\begin{matrix} 2 & 3 \\ 4 & - 2 \\ 1 & 5 \end{matrix}]$ , then

(a) only AB is defined
(b) only BA is defined
(c) AB and BA both are defined
(d) AB and BA both are not defined

Open in App

Solution

Given: $A = [\begin{matrix} 2 & - 1 & 3 \\ - 4 & 5 & 1 \end{matrix}] and B = [\begin{matrix} 2 & 3 \\ 4 & - 2 \\ 1 & 5 \end{matrix}]$
Order of A is 2 × 3 and order of B is 3 × 2.

Therefore, AB and BA both are defined.

Hence, the correct option is (c).

Suggest Corrections

Similar questions

If A, B are, respectively m × n, k × l matrices, then both AB and BA are defined if and only if

Q. If

A

and

B

are square matrices of same order satisfying

A + B = A B,

then

Q. Matrices A and B will be inverse of each other only if A. AB = BA C. AB = 0, BA = I B. AB = BA = 0 D. AB = BA = I

Choose the correct answer in the following question.
Matrices A and B will be inverse of each other only if
(a)AB=BA
(b)AB =BA =O
(c)AB=O, BA=I
(d)AB=BA =I

Q. If

A

is an

m \times n

matrix such that

A B

and

B A

are both defined, then order of

B

Join BYJU'S Learning Program

If A=2-13-451 and B=234-215, then (a) only AB is defined (b) only BA is defined (c) AB and BA both are defined (d) AB and BA both are not defined

Given: A=2-13-451 and B=234-215 Order of A is 2 × 3 and order of B is 3 × 2. Therefore, AB and BA both are defined. Hence, the correct option is (c).

If $A = [\begin{matrix} 2 & - 1 & 3 \\ - 4 & 5 & 1 \end{matrix}] and B = [\begin{matrix} 2 & 3 \\ 4 & - 2 \\ 1 & 5 \end{matrix}]$ , then

(a) only AB is defined
(b) only BA is defined
(c) AB and BA both are defined
(d) AB and BA both are not defined

Given: $A = [\begin{matrix} 2 & - 1 & 3 \\ - 4 & 5 & 1 \end{matrix}] and B = [\begin{matrix} 2 & 3 \\ 4 & - 2 \\ 1 & 5 \end{matrix}]$
Order of A is 2 × 3 and order of B is 3 × 2.

Therefore, AB and BA both are defined.

Hence, the correct option is (c).