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If \(T = \begin{pmatrix} -2 & -5 \\ 3 & 8 \end{pmatr...

If T=(2538), find T1, the inverse of T.

A.

(8532)

B.

(8532)

C.

(8532)

D.

(8532)

Correct answer is A

Let (abcd)=T1

T.T1=I

(2538)(abcd)=(1001)

2a5c=1

2b5d=0b=5d2

3a+8c=0a=8c3

3b+8d=1

2(8c3)5c=16c35c=c3=1c=3

3(5d2)+8d=15d2+8d=d2=1d=2

b=5×22=5

a=8×33=8