If A=⎣⎡2 −1 1 −3 4−3−55−4⎦⎤ and B= ⎣⎡2 −1 1 −23−2−44−3⎦⎤, show that AB=A and BA=B.

Question

If A=⎣⎡​2 −1 1 ​−3 4−3​−55−4​⎦⎤​ and B= ⎣⎡​2 −1 1 ​−23−2​−44−3​⎦⎤​, show that AB=A and BA=B.

Filo · Accepted Answer

AB=⎣⎡​2−11​−3 4−3​−55−4​⎦⎤​⎣⎡​2−11​−23−2​−44−3​⎦⎤​AB=⎣⎡​4+3−5−2−4+5 2+5−4​−4−9+10 2+12−10−2−9+8​−8−12+154+16−15−4−12+12​⎦⎤​AB=⎣⎡​2−1 1​−34−3​−55−4​⎦⎤​=ABA=⎣⎡​2−11​−23−2​−44−3​⎦⎤​⎣⎡​2−11​−3 4−3​−55−4​⎦⎤​BA=⎣⎡​4+2−4−2−3+42+2−3​−6−8+123+12−12−3−8+9​−10−10+165+15−16−5−10+12​⎦⎤​BA=⎣⎡​2−11​−23−2​−44−3​⎦⎤​=B

Question Text	If $A = ⎣ ⎡ 2 - 1 1 - 3 4 - 3 - 5 5 - 4 ⎦ ⎤$ and $B = ⎣ ⎡ 2 - 1 1 - 2 3 - 2 - 4 4 - 3 ⎦ ⎤$ , show that $A B = A$ and $B A = B$ .
Answer Type	Text solution:1
Upvotes	150

If $A = ⎣ ⎡ 2 - 1 1 - 3 4 - 3 - 5 5 - 4 ⎦ ⎤$ and $B = ⎣ ⎡ 2 - 1 1 - 2 3 - 2 - 4 4 - 3 ⎦ ⎤$ , show that $A B = A$ and $B A = B$ .

Text solutionVerified

Practice questions from similar books

If A=⎣⎡​2 −1 1 ​−3 4−3​−55−4​⎦⎤​ and B= ⎣⎡​2 −1 1 ​−23−2​−44−3​⎦⎤​, show that AB=A and BA=B.

Text solutionVerified

Practice questions from similar books

If $A = ⎣ ⎡ 2 - 1 1 - 3 4 - 3 - 5 5 - 4 ⎦ ⎤$ and $B = ⎣ ⎡ 2 - 1 1 - 2 3 - 2 - 4 4 - 3 ⎦ ⎤$ , show that $A B = A$ and $B A = B$ .