let A be a real matrix of order 2by 2 with IAI=0 and trace (A)=3. what will be the value of trace of
a. 7
b.9
c. 2
d.10
Answers
Answered by
0
Answer:
Let A=(
a
c
b
d
), abcd
=0
A
2
=(
a
c
b
d
)⋅(
a
c
b
d
)
A
2
=(
a
2
+bc
ac+cd
ab+bd
bc+d
2
)
=a
2
+ bc =1, bc +d
2
=1
ab+bd=ac+cd=0
c
=0 and b
=0=a+d=0
Trace A=a+d=0⇒a=−d
∣A∣=ad− bc =−a
2
− bc =−1
Similar questions