Matrices and Their Inverses Answers

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Which statement is true about the determinant of a matrix?

A
The determinant of a singular matrix is equal to zero.
B
The determinant of an inverse matrix is equal to zero.
C
The determinant of an identity matrix is equal to zero.
D
The determinant of a zero matrix is equal to one.
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Which value of y makes the two matrices inverses of each other?

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Dina encoded a secret phrase using matrix multiplication. She multiplied the clear text code for each letter by the matrix to get a matrix that represents the encoded text. By which matrix does Dina multiply the encoded text to get the matrix for the clear text code?

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Given matrices S and T below, which statement is true?

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A
Matrices S and T are not inverses of each other because S+T I.
Option A
B
Matrices S and T are inverses of each other because ST = TS = I.
C
Matrices S and T are inverses of each other because the determinant of S is 1.
D
Matrices S and T are not inverses of each other because the determinant of S equals the determinant of T.
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Matrices A and B are shown below. What values of x and y will make the equation AB = I true?

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If C and D are matrices and C is the inverse of D, which of the following is true?

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Which of the following matrices has an inverse?

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Yvette encoded a secret phrase using matrix multiplication. Using A = 1, B = 2, C = 3, and so on, she multiplied the clear text code for each letter by the matrix to get a matrix that represents the encoded text. The matrix representing the encoded text is . What is the secret phrase? Determine the location of spaces after you decode the text.

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A
FIND THE PRODUCT
B
FIND THE INVERSE
C
FINE IS THE PIANO
D
FINE IS A WARM DAY
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A square matrix that does not have an inverse is most specifically called a(n)

A
inverse matrix
B
identity matrix
C
singular matrix
D
non-singular matrix
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Which expression represents the inverse of the matrix below?

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