Provide an appropriate response.
-Let $M$ be a $5 \times 5$ matrix. Which of the following statements are true?
(i) $\mathrm { I } 5 \mathrm { M } = \mathrm { M }$
(ii) $\mathrm { I } _ { 5 } + \mathrm { M } = \mathrm { M }$
(iii) $\mathrm { MI } _ { 5 } = \mathrm { I } _ { 5 }$
(iv) $\mathrm { MI } _ { 5 } = \mathrm { M }$
A) (ii), (iii)
B) (i), (iii), (iv)
C) (i), (ii), (iii), (iv)
D) (i), (iv)

Question

Quizplus · Accepted Answer

(i) is true because multiplying any matrix by the identity matrix of appropriate size on the left leaves the matrix unchanged. (iv) is also true because multiplying any matrix by the identity matrix of appropriate size on the right leaves the matrix unchanged. (ii) is false because adding the identity matrix to $M$ changes its elements, not leaving $M$ unchanged. (iii) is false because it incorrectly suggests that multiplying $M$ by the identity matrix results in the identity matrix, which is not generally true unless $M$ is the inverse of the identity matrix, which is itself.

Provide an Appropriate Response MMM Be A 5×55 \times 55×5 Matrix Which of the Following Statements Are True? (I)

Provide an Appropriate Response $M$ Be A $5 \times 5$ Matrix Which of the Following Statements Are True?
(I)