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# 4-5 - 4.5 Inverse of a Square Matrix Multiplicative...

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4.5 Inverse of a Square Matrix Multiplicative identity we know that 1 a = a 1 = a (for all real numbers a ) multiplying any number by 1 yields the identical number “1” is called the multiplicative identity element for the real number system Now note: = = d c b a d c b a d c b a 1 0 0 1 1 0 0 1 so the system of 2 × 2 matrices also has an identity element, called the identity matrix , denoted by “I” In fact, the system of 3 × 3 matrices has its own identity matrix, also denoted by I. When I is mentioned, its dimension must be inferred from context. Multiplicative inverse also, for any real number a 0 there is an element a -1 , such that a a -1 = a -1 a = 1 a -1 is called the multiplicative inverse of a Q : does every square matrix A have a multiplicative inverse? That is, a matrix A -1 such that AA -1 = A -1 A = I ?

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4-5 - 4.5 Inverse of a Square Matrix Multiplicative...

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