If A and B are two matrices such that AB = B | vedclass

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(C) Given that $AB = B$ and $BA = A$.We need to find the value of ${A^2} + {B^2}$.We can write ${A^2} + {B^2} = AA + BB$.Substitute $A = BA$ and $B =

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$A + B$

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(C) Given that $AB = B$ and $BA = A$.We need to find the value of ${A^2} + {B^2}$.We can write ${A^2} + {B^2} = AA + BB$.Substitute $A = BA$ and $B = AB$ into the expression:${A^2} + {B^2} = A(BA) + B(AB)$.Using the associative property of matrix multiplication:${A^2} + {B^2} = (AB)A + (BA)B$.Since $AB = B$ and $BA = A$,we substitute these back:${A^2} + {B^2} = BA + AB$.Again,using $BA = A$ and $AB = B$:${A^2} + {B^2} = A + B$.

If $A$ and $B$ are two matrices such that $AB = B$ and $BA = A,$ then ${A^2} + {B^2} = $

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