Explanation Given Information: The provided matrices are A = [ 2 0 0 3 ] and B = [ 1 2 0 0 1 2 ] . Consider the matrices A = [ 2 0 0 3 ] and B = [ 1 2 0 0 1 2 ] . A matrix with m rows and n columns is of dimension m × n , where m and n are positive integers. Since, number of rows in A = [ 2 0 0 3 ] is 2 and number of columns is 2 . Substitute 2 for m and 2 for n in m × n . Thus, dimension of A = [ 2 0 0 3 ] is 2 × 2 . Since, number of rows in B = [ 1 2 0 0 1 2 ] is 2 and number of columns is 2 . Substitute 2 for m and 2 for n in m × n . Thus, dimension of B = [ 1 2 0 0 1 2 ] is 2 × 2 . Now, the two matrices A and B are inverse pairs if A B = I , where I is the n × n identity matrix. Since, number of columns in A is equal to the number of rows in B , the product AB is defined. For matrices A with dimension m × n and B with dimension n × k , the product AB is the matrix of dimension m × k and ij th entry of AB is the sum of product of corresponding entries of row i of A and column j of B

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Author: Stefan Waner, Steven Costenoble

Publisher: Cengage Learning

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Chapter 4.3, Problem 2E

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Whether the matrices A=[2003] and B=[120012] are inverse pairs.

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Chapter 4.3, Problem 1E

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Whether the matrices A = [ 2 0 0 3 ] and B = [ 1 2 0 0 1 2 ] are inverse pairs.

Solution Summary: The author explains that the matrices A=left[cc2& 00& 3end

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Whether the matrices A=[2003] and B=[120012] are inverse pairs.

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