If A-2-3-5-1 45 1-3-4 and B-2-2-4-1 3 4 1-2-3- show that A B-A and B A-B-

Given: #160;AB=2 3 5 1451 3 42 2 4 1341 2 3 #8658;AB=4+3 5 4 9+10 8 12+15 2 4+52+12 104+16 152+3 4 2 9+8 4 12+12 #8658;AB=2 3 5 1451 3 4 #8658;AB=ABA=2 ...

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Byju's Answer

Standard XII

Mathematics

Selecting Consecutive Terms in A.P

If A=2-3-5-1 ...

Question

If A = $[\begin{matrix} 2 & - 3 & - 5 \\ - 1 & 4 & 5 \\ 1 & - 3 & - 4 \end{matrix}]$ and B = $[\begin{matrix} 2 & - 2 & - 4 \\ - 1 & 3 & 4 \\ 1 & - 2 & - 3 \end{matrix}]$ , show that AB = A and BA = B.

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Solution

$Given : A B = [\begin{matrix} 2 & - 3 & - 5 \\ - 1 & 4 & 5 \\ 1 & - 3 & - 4 \end{matrix}] [\begin{matrix} 2 & - 2 & - 4 \\ - 1 & 3 & 4 \\ 1 & - 2 & - 3 \end{matrix}] \Rightarrow A B = [\begin{matrix} 4 + 3 - 5 & - 4 - 9 + 10 & - 8 - 12 + 15 \\ - 2 - 4 + 5 & 2 + 12 - 10 & 4 + 16 - 15 \\ 2 + 3 - 4 & - 2 - 9 + 8 & - 4 - 12 + 12 \end{matrix}] \Rightarrow A B = [\begin{matrix} 2 & - 3 & - 5 \\ - 1 & 4 & 5 \\ 1 & - 3 & - 4 \end{matrix}] \Rightarrow A B = A B A = [\begin{matrix} 2 & - 2 & - 4 \\ - 1 & 3 & 4 \\ 1 & - 2 & - 3 \end{matrix}] [\begin{matrix} 2 & - 3 & - 5 \\ - 1 & 4 & 5 \\ 1 & - 3 & - 4 \end{matrix}] \Rightarrow B A = [\begin{matrix} 4 + 2 - 4 & - 6 - 8 + 12 & - 10 - 10 + 16 \\ - 2 - 3 + 4 & 3 + 12 - 12 & 5 + 15 - 16 \\ 2 + 2 - 3 & - 3 - 8 + 9 & - 5 - 10 + 12 \end{matrix}] \Rightarrow B A = [\begin{matrix} 2 & - 2 & - 4 \\ - 1 & 3 & 4 \\ 1 & - 2 & - 3 \end{matrix}] \Rightarrow B A = B$

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Similar questions

Q. If A =

[\begin{matrix} 2 & - 3 & - 5 \\ - 1 & 4 & 5 \\ 1 & - 3 & - 4 \end{matrix}]

and B =

[\begin{matrix} - 1 & 3 & 5 \\ 1 & - 3 & - 5 \\ - 1 & 3 & 5 \end{matrix}]

, show that AB = BA = O₃_×3.

Q. Let

A = [\begin{matrix} 1 & - 2 & 3 3 & 2 & - 1 \end{matrix}]

and

B = ⎡ ⎢ ⎣ \begin{matrix} 2 & 3 - 1 & 2 4 & - 5 \end{matrix} ⎤ ⎥ ⎦

. Find AB and BA and show that

A B \neq B A .

Q. If

A = [\begin{matrix} 1 & - 2 & 3 - 4 & 2 & 5 \end{matrix}]

and

B = ⎡ ⎢ ⎣ \begin{matrix} 2 & 3 4 & 5 2 & 1 \end{matrix} ⎤ ⎥ ⎦

. Find

A B

and show that

A B \neq B A

Q. If

A = [\begin{matrix} 2 & - 3 & - 5 \\ - 1 & 4 & 5 \\ 1 & - 3 & - 4 \end{matrix}]

, show that A² = A.

Q. If

A = [\begin{matrix} 1 & - 2 & 3 - 4 & 2 & 5 \end{matrix}]

and

B = ⎡ ⎢ ⎣ \begin{matrix} 1 & 3 - 1 & 0 2 & 4 \end{matrix} ⎤ ⎥ ⎦

. Show that

(A B)^{'} = ?

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If A = 2-3-5-1 4 5 1-3-4 and B = 2-2-4-1 3 4 1-2-3, show that AB = A and BA = B.

Given: AB=2-3-5-1451-3-42-2-4-1341-2-3⇒AB=4+3-5-4-9+10-8-12+15-2-4+52+12-104+16-152+3-4-2-9+8-4-12+12⇒AB=2-3-5-1451-3-4⇒AB=ABA=2-2-4-1341-2-32-3-5-1451-3-4⇒BA=4+2-4-6-8+12-10-10+16-2-3+43+12-125+15-162+2-3-3-8+9-5-10+12⇒BA=2-2-4-1341-2-3⇒BA=B

If A = $[\begin{matrix} 2 & - 3 & - 5 \\ - 1 & 4 & 5 \\ 1 & - 3 & - 4 \end{matrix}]$ and B = $[\begin{matrix} 2 & - 2 & - 4 \\ - 1 & 3 & 4 \\ 1 & - 2 & - 3 \end{matrix}]$ , show that AB = A and BA = B.