Let A and B be square matrices of the order 3 3 . Is (AB) 2 = A 2 B 2 ? Give reasons.

Since, A and B are square matrices of order 3 3 . A B 2 = AB AB = ABAB = AABB = A 2 B 2 Therefore, A B 2 = A 2 B 2 is true when AB = BA .

Matrices — Class 12 Maths Solution

exemplar sa SA NCERT,Exemp,Q.no.30,Page 56

Question

Let A and B be square matrices of the order $3 \times 3$. Is ${(AB)^2} = {A^2}{B^2}?$ Give reasons.

Step-by-step Solution

Since, A and B are square matrices of order

$3 \times 3$.
$\therefore$ $A{B^2} = AB \cdot AB$

$= ABAB$
$= AABB$
$= {A^2}{B^2}$

Therefore, $A{B^2} = {A^2}{B^2}$ is true when $AB = BA$.

NCERT & Exemplar solution for CBSE Class 12 Mathematics, Matrices. Curated by Sachin Sharma. Free for all students.