wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

If A is an invertible matrix of order 2, then det ( A −1 ) is equal to A. det ( A ) B. C. 1 D. 0

Open in App
Solution

Let A=[ a b c d ]

The determinant of A is,

| A |=adbc

The adjoint of A is,

adjA=[ d c b a ]

It is given that A is an invertible matrix, so, A 1 exists and A 1 = 1 | A | adjA.

Substitute the values of | A | and adjA in above formula.

A 1 = 1 | A | [ d c b a ] A 1 =[ d | A | c | A | b | A | a | A | ] | A 1 |=| d | A | c | A | b | A | a | A | | | A 1 |= 1 | A | 2 | d c b a |

Simplify further,

| A 1 |= 1 | A | 2 ( adbc ) | A 1 |= 1 | A | 2 | A | | A 1 |= 1 | A | det( A 1 )= 1 det( A )

Hence, option (B) is the correct.


flag
Suggest Corrections
thumbs-up
2
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Adjoint and Inverse of a Matrix
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon