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If A is a square matrix, such that A2=A, then write the value of 7A−(I+A)3, where I is an identity matrix. - Mathematics

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If A is a square matrix, such that A2=A, then write the value of 7A(I+A)3, where I is an identity matrix.

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Solution

7A(I+A)3=7A[I3+A3+3I2A+3IA2]
=7A(I+A3+3A+3A2)                 

=7A(I+A2A+3A+3A2) 

=7A(I+AA+3A+3A)         (A2=A)

=7A(I+A2+6A) 

=7A(I+A+6A) 

=7A(I+7A) 

=7AI7A

=I
7A(I+A)3=I

Concept: Types of Matrices
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