Let A and B be square matrices of order 3 - 3 - Is AB 2- A 2 B 2 - Give reason-

Since, A and B are square matrices of the order 3 × 3. ∴ (AB)2 = AB.AB = A(BA)B = A(AB)B [If AB = BA] = AABB = A2B2 So, (AB)2 = A2B2 is true only if AB = BA. ...

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Standard XII

Mathematics

Multiplication of Matrices

Let A and B b...

Question

Let A and B be square matrices of order 3×3. Is (AB)²= A²B²? Give reason.

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Solution

Since, A and B are square matrices of the order 3 × 3.
∴ (AB)² = AB.AB
= A(BA)B
= A(AB)B [If AB = BA]
= AABB
= A²B²
So, (AB)² = A²B² is true only if AB = BA.

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Let A and B be square matrices of order 3×3. Is (AB)2 = A​​​​​​2 B​​​​​​2 ? Give reason.

Since, A and B are square matrices of the order 3 × 3. ∴ (AB)2 = AB.AB = A(BA)B = A(AB)B [If AB = BA] = AABB = A2B2 So, (AB)2 = A2B2 is true only if AB = BA.

Let A and B be square matrices of order 3×3. Is (AB)²= A²B²? Give reason.

Since, A and B are square matrices of the order 3 × 3.
∴ (AB)² = AB.AB
= A(BA)B
= A(AB)B [If AB = BA]
= AABB
= A²B²
So, (AB)² = A²B² is true only if AB = BA.