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NDA Math Matrices
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© examsnet.com
Question : 35
Total: 69
Consider the following in respect of matrices A and B of same order:
1.
A
2
−
B
2
=
(
A
+
B
)
(
A
−
B
)
2.
(
A
−
I
)
(
I
+
A
)
=
0
⇔
A
2
=
I
Where I is the identity matrix and O is the null matrix. Which of the above is/are correct?
[NDA II 2018]
1 only
2 only
Both 1 and 2
Neither 1 nor 2
Validate
Solution:
Matrix product is commutative if both are diagonal matrices of same order.
⇒
A
2
−
B
2
=
(
A
+
B
)
(
A
−
B
)
is not true
Next,
(
A
−
I
)
(
A
+
I
)
=
0
⇒
A
2
+
A
I
−
I
A
−
I
2
=
0
(
∵
A
I
=
I
A
)
⇒
A
2
=
I
2
is correct
© examsnet.com
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