If A is a square matrix, then the value of adj AT – (adj A)T is equal to

2 |A|I, where I is the identity matrix

null matrix whose order is same as that of A

unit matrix whose order is same as that of A

None of these

If A is a square matrix, then the value of adj AT – (adj A)T is equal to Correct Answer null matrix whose order is same as that of A

CONCEPT:

Adjoint Matrix:

If B_{n× n} is a cofactor matrix of matrix A_{n× n} then the adjoint matrix of A_{n× n}is denoted by adj(A) and is defined as B^T. So, adj(A) = B^T.

Property of adjoint matrix:

If A is a square matrix of order ‘n’ then adj(A^T) = (adj(A))^T

CALCULATION:

As we know that adj (A^T) = (adj (A))^T

Hence, adj (A^T) - (adj (A))^T = adj(A^T) – adj(A^T) = O (Null Matrix whose order is same as the order of A)

Feb 20, 2025

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