Question

If AB=A, BA=B then A^2
+B^2
=

Answer 1

Answer:

A+B

step by step explication ---------

1)

A^2+B^2

A.A+B.B

(AB). (AB) +(BA). (BA)

(GIVEN A=AB&B=BA)

since, the matrix multiplication is associative

hence, we can write it as

A. (BA). +B + B. (AB)A

A.B.B.+ B.A.A.

(AB).B+ (BA)A

AB+BA

A+B. = (A).----------ANSWER

2)

A and b are two matrix

If AB=AAND BA=B

Then,we have to find A^2+B^2

We fill find A^2 and B^2

A^2=A×A=A (BA)

B^2=B×B=B (AB)

If A and B are matrix means (AB=BA)

Therefore, A^2=A (BA)=A (AB)=AB=B

B^2=B (AB)=B (BA)=BA=A

Therefore , A^2=B^2=A+B

(A+B)---------ANSWER

Answer 2

:- A+ B is the your answer

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