7. Let A and B two 3-by-3 matrices, with |B| = 1. Let C be the inverse matrix of B. Which of the following statements is true? Mark only one oval. 0001 If |A|+ 12B| = 8, then the matrix A is nonsingular. A^2 and A have the same rank only if A is an idempotent matrix. If A is idempotent, the matrix I - BAC is also idempotent. The matrix BAC is idempotent. The matrix BAC is invertible.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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7. Let A and B two 3-by-3 matrices, with |B| = 1. Let C be the inverse matrix of B.
Which of the following statements is true?
Mark only one oval.
1000
If |A| + |2B| = 8, then the matrix A is nonsingular.
A^2 and A have the same rank only if A is an idempotent matrix.
If A is idempotent, the matrix I - BAC is also idempotent.
The matrix BAC is idempotent.
The matrix BAC is invertible.
Transcribed Image Text:7. Let A and B two 3-by-3 matrices, with |B| = 1. Let C be the inverse matrix of B. Which of the following statements is true? Mark only one oval. 1000 If |A| + |2B| = 8, then the matrix A is nonsingular. A^2 and A have the same rank only if A is an idempotent matrix. If A is idempotent, the matrix I - BAC is also idempotent. The matrix BAC is idempotent. The matrix BAC is invertible.
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