Question

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.​

Answer 1

Answer:

$<marquee><strong>VALUE</strong> <strong>O</strong><strong>F</strong><strong> </strong>-->7A - ( l + A )³ =</marquee>$

$\boxed{= 7A - (l³+A³+ 3 x l² x A + 3x l x A³)}$

= 7A - (l³+A³+ 3 x l² x A + 3x l x A³)

= 7A- ( l + A³+ 3A + 3A² )

= 7A - ( l x A x A² + 3A + 3A² )

Coz ...A²= A

= 7A - ( l + A x A + 3A +3A )

= 7A - ( l + A² + 3A + 3A )

= 7A - ( l + A + 6A )

= 7A - ( l + 7A )

= 7A - l - 7A

$\bold{\huge{\fbox{\color{green}{= -l}}}}$

Answer 2

Answer:

given A2=A

7A−(I+A)3=7A−[I3+3A2I+3AI2+A3]

=7A−[I+3A+3A+A2.A]

=7A−[I+3A+3A+A]

=7A−I+7A

=−I