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Question:
Let A and B be orthogonal and det A+det B=0. Then
Let A and B be orthogonal and det A+det B=0. Then
Updated On: Apr 28, 2024
- A+B is singular
- A+B is non-singular
- A+B is orthogonal
- A+B is skew-symmetric
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The Correct Option is A
Solution and Explanation
The correct answer is option (A): A+B is singular
AAT=I \(\Rightarrow\) |A|=\(\pm 1\)
If |A|=1 then |B|=-1
Then |A+B|=0
So, A+B is singular
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Concepts Used:
Matrix Transformation
The numbers or functions that are kept in a matrix are termed the elements or the entries of the matrix.
Transpose Matrix:
The matrix acquired by interchanging the rows and columns of the parent matrix is termed the Transpose matrix. The definition of a transpose matrix goes as follows - “A Matrix which is devised by turning all the rows of a given matrix into columns and vice-versa.”
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